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BT 34.016 358.342 Td /F1 16.5 Tf [(The Arithmetic Of Dynamical Systems Graduate Texts In Mathematics )] TJ ET
BT 34.016 338.196 Td /F1 16.5 Tf [(241 By Silverman Joseph H Author Jun 06 2007 Hardcover)] TJ ET
BT 34.016 306.803 Td /F1 8.2 Tf [(When people should go to the books stores, search creation by shop, shelf by shelf, it is essentially problematic. This is why we allow the )] TJ ET
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BT 277.036 296.729 Td /F1 8.2 Tf [(The Arithmetic Of Dynamical Systems Graduate Texts In Mathematics 241 )] TJ ET
BT 34.016 286.656 Td /F1 8.2 Tf [(By Silverman Joseph H Author Jun 06 2007 Hardcover)] TJ ET
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BT 34.016 266.683 Td /F1 8.2 Tf [(By searching the title, publisher, or authors of guide you truly want, you can discover them rapidly. In the house, workplace, or perhaps in your )] TJ ET
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BT 34.016 246.536 Td /F1 8.2 Tf [(Texts In Mathematics 241 By Silverman Joseph H Author Jun 06 2007 Hardcover, it is very simple then, in the past currently we extend the )] TJ ET
BT 34.016 236.463 Td /F1 8.2 Tf [(member to purchase and create bargains to download and install The Arithmetic Of Dynamical Systems Graduate Texts In Mathematics 241 By )] TJ ET
BT 34.016 226.390 Td /F1 8.2 Tf [(Silverman Joseph H Author Jun 06 2007 Hardcover in view of that simple!)] TJ ET
BT 34.016 189.917 Td /F1 8.2 Tf [(Moduli Spaces and Arithmetic Dynamics)] TJ ET
BT 181.641 189.917 Td /F1 8.2 Tf [( Joseph H. Silverman )] TJ ET
BT 34.016 179.843 Td /F1 8.2 Tf [(Operator Theoretic Aspects of Ergodic Theory)] TJ ET
BT 202.291 179.843 Td /F1 8.2 Tf [( Tanja Eisner 2015-11-18 Stunning recent results by Host–Kra, Green–Tao, and others, highlight )] TJ ET
BT 34.016 169.770 Td /F1 8.2 Tf [(the timeliness of this systematic introduction to classical ergodic theory using the tools of operator theory. Assuming no prior exposure to )] TJ ET
BT 34.016 159.697 Td /F1 8.2 Tf [(ergodic theory, this book provides a modern foundation for introductory courses on ergodic theory, especially for students or researchers with )] TJ ET
BT 34.016 149.624 Td /F1 8.2 Tf [(an interest in functional analysis. While basic analytic notions and results are reviewed in several appendices, more advanced operator )] TJ ET
BT 34.016 139.550 Td /F1 8.2 Tf [(theoretic topics are developed in detail, even beyond their immediate connection with ergodic theory. As a consequence, the book is also )] TJ ET
BT 34.016 129.477 Td /F1 8.2 Tf [(suitable for advanced or special-topic courses on functional analysis with applications to ergodic theory. Topics include: • an intuitive )] TJ ET
BT 34.016 119.404 Td /F1 8.2 Tf [(introduction to ergodic theory • an introduction to the basic notions, constructions, and standard examples of topological dynamical systems • )] TJ ET
BT 34.016 109.331 Td /F1 8.2 Tf [(Koopman operators, Banach lattices, lattice and algebra homomorphisms, and the Gelfand–Naimark theorem • measure-preserving dynamical )] TJ ET
BT 34.016 99.257 Td /F1 8.2 Tf [(systems • von Neumann’s Mean Ergodic Theorem and Birkhoff’s Pointwise Ergodic Theorem • strongly and weakly mixing systems • an )] TJ ET
BT 34.016 89.184 Td /F1 8.2 Tf [(examination of notions of isomorphism for measure-preserving systems • Markov operators, and the related concept of a factor of a measure )] TJ ET
BT 34.016 79.111 Td /F1 8.2 Tf [(preserving system • compact groups and semigroups, and a powerful tool in their study, the Jacobs–de Leeuw–Glicksberg decomposition • an )] TJ ET
BT 34.016 69.038 Td /F1 8.2 Tf [(introduction to the spectral theory of dynamical systems, the theorems of Furstenberg and Weiss on multiple recurrence, and applications of )] TJ ET
BT 34.016 58.964 Td /F1 8.2 Tf [(dynamical systems to combinatorics \(theorems of van der Waerden, Gallai,and Hindman, Furstenberg’s Correspondence Principle, theorems of )] TJ ET
BT 34.016 48.891 Td /F1 8.2 Tf [(Roth and Furstenberg–Sárközy\) Beyond its use in the classroom, Operator Theoretic Aspects of Ergodic Theory can serve as a valuable )] TJ ET
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BT 34.016 377.456 Td /F1 8.2 Tf [(foundation for doing research at the intersection of ergodic theory and operator theory)] TJ ET
BT 34.016 367.382 Td /F1 8.2 Tf [(Nilpotent Structures in Ergodic Theory)] TJ ET
BT 173.399 367.382 Td /F1 8.2 Tf [( Bernard Host 2018-12-12 Nilsystems play a key role in the structure theory of measure preserving )] TJ ET
BT 34.016 357.309 Td /F1 8.2 Tf [(systems, arising as the natural objects that describe the behavior of multiple ergodic averages. This book is a comprehensive treatment of their )] TJ ET
BT 34.016 347.236 Td /F1 8.2 Tf [(role in ergodic theory, covering development of the abstract theory leading to the structural statements, applications of these results, and )] TJ ET
BT 34.016 337.163 Td /F1 8.2 Tf [(connections to other fields. Starting with a summary of the relevant dynamical background, the book methodically develops the theory of cubic )] TJ ET
BT 34.016 327.089 Td /F1 8.2 Tf [(structures that give rise to nilpotent groups and reviews results on nilsystems and their properties that are scattered throughout the literature. )] TJ ET
BT 34.016 317.016 Td /F1 8.2 Tf [(These basic ingredients lay the groundwork for the ergodic structure theorems, and the book includes numerous formulations of these deep )] TJ ET
BT 34.016 306.943 Td /F1 8.2 Tf [(results, along with detailed proofs. The structure theorems have many applications, both in ergodic theory and in related fields; the book )] TJ ET
BT 34.016 296.870 Td /F1 8.2 Tf [(develops the connections to topological dynamics, combinatorics, and number theory, including an overview of the role of nilsystems in each of )] TJ ET
BT 34.016 286.796 Td /F1 8.2 Tf [(these areas. The final section is devoted to applications of the structure theory, covering numerous convergence and recurrence results. The )] TJ ET
BT 34.016 276.723 Td /F1 8.2 Tf [(book is aimed at graduate students and researchers in ergodic theory, along with those who work in the related areas of arithmetic )] TJ ET
BT 34.016 266.650 Td /F1 8.2 Tf [(combinatorics, harmonic analysis, and number theory.)] TJ ET
BT 34.016 256.577 Td /F1 8.2 Tf [(An Experimental Introduction to Number Theory)] TJ ET
BT 208.709 256.577 Td /F1 8.2 Tf [( Benjamin Hutz 2018-04-17 This book presents material suitable for an undergraduate course in )] TJ ET
BT 34.016 246.503 Td /F1 8.2 Tf [(elementary number theory from a computational perspective. It seeks to not only introduce students to the standard topics in elementary )] TJ ET
BT 34.016 236.430 Td /F1 8.2 Tf [(number theory, such as prime factorization and modular arithmetic, but also to develop their ability to formulate and test precise conjectures )] TJ ET
BT 34.016 226.357 Td /F1 8.2 Tf [(from experimental data. Each topic is motivated by a question to be answered, followed by some experimental data, and, finally, the statement )] TJ ET
BT 34.016 216.284 Td /F1 8.2 Tf [(and proof of a theorem. There are numerous opportunities throughout the chapters and exercises for the students to engage in \(guided\) open-)] TJ ET
BT 34.016 206.210 Td /F1 8.2 Tf [(ended exploration. At the end of a course using this book, the students will understand how mathematics is developed from asking questions to )] TJ ET
BT 34.016 196.137 Td /F1 8.2 Tf [(gathering data to formulating and proving theorems. The mathematical prerequisites for this book are few. Early chapters contain topics such as )] TJ ET
BT 34.016 186.064 Td /F1 8.2 Tf [(integer divisibility, modular arithmetic, and applications to cryptography, while later chapters contain more specialized topics, such as )] TJ ET
BT 34.016 175.991 Td /F1 8.2 Tf [(Diophantine approximation, number theory of dynamical systems, and number theory with polynomials. Students of all levels will be drawn in by )] TJ ET
BT 34.016 165.917 Td /F1 8.2 Tf [(the patterns and relationships of number theory uncovered through data driven exploration.)] TJ ET
BT 34.016 155.844 Td /F1 8.2 Tf [(An Introduction To Chaotic Dynamical Systems)] TJ ET
BT 206.408 155.844 Td /F1 8.2 Tf [( Robert Devaney 2018-03-09 The study of nonlinear dynamical systems has exploded in the )] TJ ET
BT 34.016 145.771 Td /F1 8.2 Tf [(past 25 years, and Robert L. Devaney has made these advanced research developments accessible to undergraduate and graduate )] TJ ET
BT 34.016 135.698 Td /F1 8.2 Tf [(mathematics students as well as researchers in other disciplines with the introduction of this widely praised book. In this second edition of his )] TJ ET
BT 34.016 125.624 Td /F1 8.2 Tf [(best-selling text, Devaney includes new material on the orbit diagram fro maps of the interval and the Mandelbrot set, as well as striking color )] TJ ET
BT 34.016 115.551 Td /F1 8.2 Tf [(photos illustrating both Julia and Mandelbrot sets. This book assumes no prior acquaintance with advanced mathematical topics such as )] TJ ET
BT 34.016 105.478 Td /F1 8.2 Tf [(measure theory, topology, and differential geometry. Assuming only a knowledge of calculus, Devaney introduces many of the basic concepts )] TJ ET
BT 34.016 95.405 Td /F1 8.2 Tf [(of modern dynamical systems theory and leads the reader to the point of current research in several areas.)] TJ ET
BT 34.016 85.331 Td /F1 8.2 Tf [(Potential Theory and Dynamics on the Berkovich Projective Line)] TJ ET
BT 268.778 85.331 Td /F1 8.2 Tf [( Matthew Baker 2010-03-10 The purpose of this book is to develop the )] TJ ET
BT 34.016 75.258 Td /F1 8.2 Tf [(foundations of potential theory and rational dynamics on the Berkovich projective line over an arbitrary complete, algebraically closed non-)] TJ ET
BT 34.016 65.185 Td /F1 8.2 Tf [(Archimedean field. In addition to providing a concrete and ``elementary'' introduction to Berkovich analytic spaces and to potential theory and )] TJ ET
BT 34.016 55.112 Td /F1 8.2 Tf [(rational iteration on the Berkovich line, the book contains applications to arithmetic geometry and arithmetic dynamics. A number of results in )] TJ ET
BT 34.016 45.038 Td /F1 8.2 Tf [(the book are new, and most have not previously appeared in book form. Three appendices--on analysis, $\\mathbb{R}$-trees, and Berkovich's )] TJ ET
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BT 34.016 377.456 Td /F1 8.2 Tf [(general theory of analytic spaces--are included to make the book as self-contained as possible. The authors first give a detailed description of )] TJ ET
BT 34.016 367.382 Td /F1 8.2 Tf [(the topological structure of the Berkovich projective line and then introduce the Hsia kernel, the fundamental kernel for potential theory. Using )] TJ ET
BT 34.016 357.309 Td /F1 8.2 Tf [(the theory of metrized graphs, they define a Laplacian operator on the Berkovich line and construct theories of capacities, harmonic and )] TJ ET
BT 34.016 347.236 Td /F1 8.2 Tf [(subharmonic functions, and Green's functions, all of which are strikingly similar to their classical complex counterparts. After developing a )] TJ ET
BT 34.016 337.163 Td /F1 8.2 Tf [(theory of multiplicities for rational functions, they give applications to non-Archimedean dynamics, including local and global equidistribution )] TJ ET
BT 34.016 327.089 Td /F1 8.2 Tf [(theorems, fixed point theorems, and Berkovich space analogues of many fundamental results from the classical Fatou-Julia theory of rational )] TJ ET
BT 34.016 317.016 Td /F1 8.2 Tf [(iteration. They illustrate the theory with concrete examples and exposit Rivera-Letelier's results concerning rational dynamics over the field of )] TJ ET
BT 34.016 306.943 Td /F1 8.2 Tf [($p$-adic complex numbers. They also establish Berkovich space versions of arithmetic results such as the Fekete-Szego theorem and Bilu's )] TJ ET
BT 34.016 296.870 Td /F1 8.2 Tf [(equidistribution theorem.)] TJ ET
BT 34.016 286.796 Td /F1 8.2 Tf [(Fifth International Congress of Chinese Mathematicians)] TJ ET
0.000 0.000 0.000 RG
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34.016 285.435 m 237.139 285.435 l S
BT 237.139 286.796 Td /F1 8.2 Tf [( Lizhen Ji 2012 This two-part volume represents the proceedings of the Fifth )] TJ ET
BT 34.016 276.723 Td /F1 8.2 Tf [(International Congress of Chinese Mathematicians, held at Tsinghua University, Beijing, in December 2010. The Congress brought together )] TJ ET
BT 34.016 266.650 Td /F1 8.2 Tf [(eminent Chinese and overseas mathematicians to discuss the latest developments in pure and applied mathematics. Included are 60 papers )] TJ ET
BT 34.016 256.577 Td /F1 8.2 Tf [(based on lectures given at the conference.)] TJ ET
BT 34.016 246.503 Td /F1 8.2 Tf [(Frontiers in Complex Dynamics)] TJ ET
0.165 w 0 J [ ] 0 d
34.016 245.142 m 148.616 245.142 l S
BT 148.616 246.503 Td /F1 8.2 Tf [( Araceli Bonifant 2014-03-16 John Milnor, best known for his work in differential topology, K-theory, and )] TJ ET
BT 34.016 236.430 Td /F1 8.2 Tf [(dynamical systems, is one of only three mathematicians to have won the Fields medal, the Abel prize, and the Wolf prize, and is the only one to )] TJ ET
BT 34.016 226.357 Td /F1 8.2 Tf [(have received all three of the Leroy P. Steele prizes. In honor of his eightieth birthday, this book gathers together surveys and papers inspired )] TJ ET
BT 34.016 216.284 Td /F1 8.2 Tf [(by Milnor's work, from distinguished experts examining not only holomorphic dynamics in one and several variables, but also differential )] TJ ET
BT 34.016 206.210 Td /F1 8.2 Tf [(geometry, entropy theory, and combinatorial group theory. The book contains the last paper written by William Thurston, as well as a short )] TJ ET
BT 34.016 196.137 Td /F1 8.2 Tf [(paper by John Milnor himself. Introductory sections put the papers in mathematical and historical perspective, color figures are included, and an )] TJ ET
BT 34.016 186.064 Td /F1 8.2 Tf [(index facilitates browsing. This collection will be useful to students and researchers for decades to come. The contributors are Marco Abate, )] TJ ET
BT 34.016 175.991 Td /F1 8.2 Tf [(Marco Arizzi, Alexander Blokh, Thierry Bousch, Xavier Buff, Serge Cantat, Tao Chen, Robert Devaney, Alexandre Dezotti, Tien-Cuong Dinh, )] TJ ET
BT 34.016 165.917 Td /F1 8.2 Tf [(Romain Dujardin, Hugo García-Compeán, William Goldman, Rotislav Grigorchuk, John Hubbard, Yunping Jiang, Linda Keen, Jan Kiwi, Genadi )] TJ ET
BT 34.016 155.844 Td /F1 8.2 Tf [(Levin, Daniel Meyer, John Milnor, Carlos Moreira, Vincente Muñoz, Viet-Anh Nguyên, Lex Oversteegen, Ricardo Pérez-Marco, Ross Ptacek, )] TJ ET
BT 34.016 145.771 Td /F1 8.2 Tf [(Jasmin Raissy, Pascale Roesch, Roberto Santos-Silva, Dierk Schleicher, Nessim Sibony, Daniel Smania, Tan Lei, William Thurston, Vladlen )] TJ ET
BT 34.016 135.698 Td /F1 8.2 Tf [(Timorin, Sebastian van Strien, and Alberto Verjovsky.)] TJ ET
BT 34.016 125.624 Td /F1 8.2 Tf [(Algebraic and Topological Dynamics)] TJ ET
0.165 w 0 J [ ] 0 d
34.016 124.263 m 167.435 124.263 l S
BT 167.435 125.624 Td /F1 8.2 Tf [( S. F. Koli?ada 2005 This volume contains a collection of articles from the special program on algebraic )] TJ ET
BT 34.016 115.551 Td /F1 8.2 Tf [(and topological dynamics and a workshop on dynamical systems held at the Max-Planck Institute \(Bonn, Germany\). It reflects the extraordinary )] TJ ET
BT 34.016 105.478 Td /F1 8.2 Tf [(vitality of dynamical systems in its interaction with a broad range of mathematical subjects. Topics covered in the book include asymptotic )] TJ ET
BT 34.016 95.405 Td /F1 8.2 Tf [(geometric analysis, transformation groups, arithmetic dynamics, complex dynamics, symbolic dynamics, statistical properties of dynamical )] TJ ET
BT 34.016 85.331 Td /F1 8.2 Tf [(systems, and the theory of entropy and chaos. The book is suitable for graduate students and researchers interested in dynamical systems.)] TJ ET
BT 34.016 75.258 Td /F1 8.2 Tf [(Dynamical Systems and Ergodic Theory)] TJ ET
0.165 w 0 J [ ] 0 d
34.016 73.897 m 180.725 73.897 l S
BT 180.725 75.258 Td /F1 8.2 Tf [( Mark Pollicott 1998-01-29 This book is an introduction to topological dynamics and ergodic theory. It is )] TJ ET
BT 34.016 65.185 Td /F1 8.2 Tf [(divided into a number of relatively short chapters with the intention that each may be used as a component of a lecture course tailored to the )] TJ ET
BT 34.016 55.112 Td /F1 8.2 Tf [(particular audience. The authors provide a number of applications, principally to number theory and arithmetic progressions \(through Van der )] TJ ET
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BT 34.016 377.456 Td /F1 8.2 Tf [(Waerden's theorem and Szemerdi's theorem\). This text is suitable for advanced undergraduate and beginning graduate students.)] TJ ET
BT 34.016 367.382 Td /F1 8.2 Tf [(Chaos and Dynamical Systems)] TJ ET
BT 148.633 367.382 Td /F1 8.2 Tf [( David Feldman 2019-08-06 The author presents an accessible, clear introduction to dynamical systems and )] TJ ET
BT 34.016 357.309 Td /F1 8.2 Tf [(chaos theory, important and exciting areas that have shaped many scientific fields. While the rules governing dynamical systems are well-)] TJ ET
BT 34.016 347.236 Td /F1 8.2 Tf [(specified and simple, the behavior of many dynamical systems is remarkably complex.)] TJ ET
BT 34.016 337.163 Td /F1 8.2 Tf [(Dynamical Numbers: Interplay between Dynamical Systems and Number Theory)] TJ ET
0.165 w 0 J [ ] 0 d
34.016 335.801 m 328.351 335.801 l S
BT 328.351 337.163 Td /F1 8.2 Tf [( S. F. Koli?a?da 2010 This volume contains papers from the )] TJ ET
BT 34.016 327.089 Td /F1 8.2 Tf [(special program and international conference on Dynamical Numbers which were held at the Max-Planck Institute in Bonn, Germany in 2009. )] TJ ET
BT 34.016 317.016 Td /F1 8.2 Tf [(These papers reflect the extraordinary range and depth of the interactions between ergodic theory and dynamical systems and number theory. )] TJ ET
BT 34.016 306.943 Td /F1 8.2 Tf [(Topics covered in the book include stationary measures, systems of enumeration, geometrical methods, spectral methods, and algebraic )] TJ ET
BT 34.016 296.870 Td /F1 8.2 Tf [(dynamical systems.)] TJ ET
BT 34.016 286.796 Td /F1 8.2 Tf [(The Arithmetic of Elliptic Curves)] TJ ET
0.165 w 0 J [ ] 0 d
34.016 285.435 m 150.918 285.435 l S
BT 150.918 286.796 Td /F1 8.2 Tf [( Joseph H. Silverman 2013-03-09 The theory of elliptic curves is distinguished by its long history and by the )] TJ ET
BT 34.016 276.723 Td /F1 8.2 Tf [(diversity of the methods that have been used in its study. This book treats the arithmetic approach in its modern formulation, through the use of )] TJ ET
BT 34.016 266.650 Td /F1 8.2 Tf [(basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book )] TJ ET
BT 34.016 256.577 Td /F1 8.2 Tf [(proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local )] TJ ET
BT 34.016 246.503 Td /F1 8.2 Tf [(fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y )] TJ ET
BT 34.016 236.430 Td /F1 8.2 Tf [(= X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more )] TJ ET
BT 34.016 226.357 Td /F1 8.2 Tf [(advanced topics.)] TJ ET
BT 34.016 216.284 Td /F1 8.2 Tf [(Ergodic Theory)] TJ ET
0.165 w 0 J [ ] 0 d
34.016 214.922 m 89.951 214.922 l S
BT 89.951 216.284 Td /F1 8.2 Tf [( Manfred Einsiedler 2010-09-11 This text is a rigorous introduction to ergodic theory, developing the machinery of conditional )] TJ ET
BT 34.016 206.210 Td /F1 8.2 Tf [(measures and expectations, mixing, and recurrence. Beginning by developing the basics of ergodic theory and progressing to describe some )] TJ ET
BT 34.016 196.137 Td /F1 8.2 Tf [(recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl's polynomial )] TJ ET
BT 34.016 186.064 Td /F1 8.2 Tf [(equidistribution theorem, the ergodic proof of Szemeredi's theorem, the connection between the continued fraction map and the modular )] TJ ET
BT 34.016 175.991 Td /F1 8.2 Tf [(surface, and a proof of the equidistribution of horocycle orbits. Ergodic Theory with a view towards Number Theory will appeal to )] TJ ET
BT 34.016 165.917 Td /F1 8.2 Tf [(mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is )] TJ ET
BT 34.016 155.844 Td /F1 8.2 Tf [(assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and )] TJ ET
BT 34.016 145.771 Td /F1 8.2 Tf [(researchers in ergodic theory, homogenous dynamics or number theory.)] TJ ET
BT 34.016 135.698 Td /F1 8.2 Tf [(Dynamics: Topology and Numbers)] TJ ET
0.165 w 0 J [ ] 0 d
34.016 134.336 m 160.554 134.336 l S
BT 160.554 135.698 Td /F1 8.2 Tf [( Pieter Moree 2020-02-12 This volume contains the proceedings of the conference Dynamics: Topology and )] TJ ET
BT 34.016 125.624 Td /F1 8.2 Tf [(Numbers, held from July 2–6, 2018, at the Max Planck Institute for Mathematics, Bonn, Germany.? The papers cover diverse fields of )] TJ ET
BT 34.016 115.551 Td /F1 8.2 Tf [(mathematics with a unifying theme of relation to dynamical systems. These include arithmetic geometry, flat geometry, complex dynamics, )] TJ ET
BT 34.016 105.478 Td /F1 8.2 Tf [(graph theory, relations to number theory, and topological dynamics. The volume is dedicated to the memory of Sergiy Kolyada and also )] TJ ET
BT 34.016 95.405 Td /F1 8.2 Tf [(contains some personal accounts of his life and mathematics.)] TJ ET
BT 34.016 85.331 Td /F1 8.2 Tf [(Heights of Polynomials and Entropy in Algebraic Dynamics)] TJ ET
BT 248.590 85.331 Td /F1 8.2 Tf [( Graham Everest 2013-06-29 The main theme of this book is the theory of heights as )] TJ ET
BT 34.016 75.258 Td /F1 8.2 Tf [(they appear in various guises. This includes a large body of results on Mahlers measure of the height of a polynomial. The authors'approach is )] TJ ET
BT 34.016 65.185 Td /F1 8.2 Tf [(very down to earth as they cover the rationals, assuming no prior knowledge of elliptic curves. The chapters include examples and particular )] TJ ET
BT 34.016 55.112 Td /F1 8.2 Tf [(computations, with all special calculation included so as to be self-contained. The authors devote space to discussing Mahlers measure and to )] TJ ET
BT 34.016 45.038 Td /F1 8.2 Tf [(giving some convincing and original examples to explain this phenomenon. XXXXXXX NEUER TEXT The main theme of this book is the theory )] TJ ET
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BT 34.016 377.456 Td /F1 8.2 Tf [(of heights as it appears in various guises. To this §End.txt.Int.:, it examines the results of Mahlers measure of the height of a polynomial, which )] TJ ET
BT 34.016 367.382 Td /F1 8.2 Tf [(have never before appeared in book form. The authors take a down-to-earth approach that includes convincing and original examples. The )] TJ ET
BT 34.016 357.309 Td /F1 8.2 Tf [(book uncovers new and interesting connections between number theory and dynamics and will be interesting to researchers in both number )] TJ ET
BT 34.016 347.236 Td /F1 8.2 Tf [(theory and nonlinear dynamics.)] TJ ET
BT 34.016 337.163 Td /F1 8.2 Tf [(Advanced Topics in the Arithmetic of Elliptic Curves)] TJ ET
BT 222.454 337.163 Td /F1 8.2 Tf [( Joseph H. Silverman 2013-12-01 In the introduction to the first volume of The Arithmetic of )] TJ ET
BT 34.016 327.089 Td /F1 8.2 Tf [(Elliptic Curves \(Springer-Verlag, 1986\), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, )] TJ ET
BT 34.016 317.016 Td /F1 8.2 Tf [("many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit )] TJ ET
BT 34.016 306.943 Td /F1 8.2 Tf [(understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out )] TJ ET
BT 34.016 296.870 Td /F1 8.2 Tf [(that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is )] TJ ET
BT 34.016 286.796 Td /F1 8.2 Tf [(covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces )] TJ ET
BT 34.016 276.723 Td /F1 8.2 Tf [(and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-)] TJ ET
BT 34.016 266.650 Td /F1 8.2 Tf [(discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of canonical local height functions.)] TJ ET
BT 34.016 256.577 Td /F1 8.2 Tf [(Trilogy of Numbers and Arithmetic - Book 1: History of Numbers and Arithmetic: An Information Perspective)] TJ ET
BT 425.561 256.577 Td /F1 8.2 Tf [( Mark Burgin )] TJ ET
BT 34.016 246.503 Td /F1 8.2 Tf [(Introduction to Dynamics)] TJ ET
0.165 w 0 J [ ] 0 d
34.016 245.142 m 124.799 245.142 l S
BT 124.799 246.503 Td /F1 8.2 Tf [( I. C. Percival 1982-12-02 In this book, the subject of dynamics is introduced at undergraduate level through the )] TJ ET
BT 34.016 236.430 Td /F1 8.2 Tf [(elementary qualitative theory of differential equations, the geometry of phase curves and the theory of stability. The text is supplemented with )] TJ ET
BT 34.016 226.357 Td /F1 8.2 Tf [(over a hundred exercises.)] TJ ET
BT 34.016 216.284 Td /F1 8.2 Tf [(Dynamics in One Non-Archimedean Variable)] TJ ET
BT 198.149 216.284 Td /F1 8.2 Tf [( Robert L. Benedetto 2019-03-05 The theory of complex dynamics in one variable, initiated by )] TJ ET
BT 34.016 206.210 Td /F1 8.2 Tf [(Fatou and Julia in the early twentieth century, concerns the iteration of a rational function acting on the Riemann sphere. Building on )] TJ ET
BT 34.016 196.137 Td /F1 8.2 Tf [(foundational investigations of p-adic dynamics in the late twentieth century, dynamics in one non-archimedean variable is the analogous theory )] TJ ET
BT 34.016 186.064 Td /F1 8.2 Tf [(over non-archimedean fields rather than over the complex numbers. It is also an essential component of the number-theoretic study of )] TJ ET
BT 34.016 175.991 Td /F1 8.2 Tf [(arithmetic dynamics. This textbook presents the fundamentals of non-archimedean dynamics, including a unified exposition of Rivera-Letelier's )] TJ ET
BT 34.016 165.917 Td /F1 8.2 Tf [(classification theorem, as well as results on wandering domains, repelling periodic points, and equilibrium measures. The Berkovich projective )] TJ ET
BT 34.016 155.844 Td /F1 8.2 Tf [(line, which is the appropriate setting for the associated Fatou and Julia sets, is developed from the ground up, as are relevant results in non-)] TJ ET
BT 34.016 145.771 Td /F1 8.2 Tf [(archimedean analysis. The presentation is accessible to graduate students with only first-year courses in algebra and analysis under their belts, )] TJ ET
BT 34.016 135.698 Td /F1 8.2 Tf [(although some previous exposure to non-archimedean fields, such as the p-adic numbers, is recommended. The book should also be a useful )] TJ ET
BT 34.016 125.624 Td /F1 8.2 Tf [(reference for more advanced students and researchers in arithmetic and non-archimedean dynamics.)] TJ ET
BT 34.016 115.551 Td /F1 8.2 Tf [(Ultrametric Pseudodifferential Equations and Applications)] TJ ET
BT 244.019 115.551 Td /F1 8.2 Tf [( Andrei Yu. Khrennikov 2018-04-26 Starting from physical motivations and leading to )] TJ ET
BT 34.016 105.478 Td /F1 8.2 Tf [(practical applications, this book provides an interdisciplinary perspective on the cutting edge of ultrametric pseudodifferential equations. It )] TJ ET
BT 34.016 95.405 Td /F1 8.2 Tf [(shows the ways in which these equations link different fields including mathematics, engineering, and geophysics. In particular, the authors )] TJ ET
BT 34.016 85.331 Td /F1 8.2 Tf [(provide a detailed explanation of the geophysical applications of p-adic diffusion equations, useful when modeling the flows of liquids through )] TJ ET
BT 34.016 75.258 Td /F1 8.2 Tf [(porous rock. p-adic wavelets theory and p-adic pseudodifferential equations are also presented, along with their connections to mathematical )] TJ ET
BT 34.016 65.185 Td /F1 8.2 Tf [(physics, representation theory, the physics of disordered systems, probability, number theory, and p-adic dynamical systems. Material that was )] TJ ET
BT 34.016 55.112 Td /F1 8.2 Tf [(previously spread across many articles in journals of many different fields is brought together here, including recent work on the van der Put )] TJ ET
BT 34.016 45.038 Td /F1 8.2 Tf [(series technique. This book provides an excellent snapshot of the fascinating field of ultrametric pseudodifferential equations, including their )] TJ ET
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BT 34.016 377.456 Td /F1 8.2 Tf [(emerging applications and currently unsolved problems.)] TJ ET
BT 34.016 367.382 Td /F1 8.2 Tf [(Advances in Ultrametric Analysis)] TJ ET
BT 154.127 367.382 Td /F1 8.2 Tf [( Alain Escassut 2018-03-26 Articles included in this book feature recent developments in various areas of non-)] TJ ET
BT 34.016 357.309 Td /F1 8.2 Tf [(Archimedean analysis: summation of -adic series, rational maps on the projective line over , non-Archimedean Hahn-Banach theorems, )] TJ ET
BT 34.016 347.236 Td /F1 8.2 Tf [(ultrametric Calkin algebras, -modules with a convex base, non-compact Trace class operators and Schatten-class operators in -adic Hilbert )] TJ ET
BT 34.016 337.163 Td /F1 8.2 Tf [(spaces, algebras of strictly differentiable functions, inverse function theorem and mean value theorem in Levi-Civita fields, ultrametric spectra of )] TJ ET
BT 34.016 327.089 Td /F1 8.2 Tf [(commutative non-unital Banach rings, classes of non-Archimedean Köthe spaces, -adic Nevanlinna theory and applications, and sub-)] TJ ET
BT 34.016 317.016 Td /F1 8.2 Tf [(coordinate representation of -adic functions. Moreover, a paper on the history of -adic analysis with a comparative summary of non-)] TJ ET
BT 34.016 306.943 Td /F1 8.2 Tf [(Archimedean fields is presented. Through a combination of new research articles and a survey paper, this book provides the reader with an )] TJ ET
BT 34.016 296.870 Td /F1 8.2 Tf [(overview of current developments and techniques in non-Archimedean analysis as well as a broad knowledge of some of the sub-areas of this )] TJ ET
BT 34.016 286.796 Td /F1 8.2 Tf [(exciting and fast-developing research area.)] TJ ET
BT 34.016 276.723 Td /F1 8.2 Tf [(The Arithmetic of Elliptic Curves)] TJ ET
0.165 w 0 J [ ] 0 d
34.016 275.362 m 150.918 275.362 l S
BT 150.918 276.723 Td /F1 8.2 Tf [( Joseph H. Silverman 2009-04-20 The theory of elliptic curves is distinguished by its long history and by the )] TJ ET
BT 34.016 266.650 Td /F1 8.2 Tf [(diversity of the methods that have been used in its study. This book treats the arithmetic approach in its modern formulation, through the use of )] TJ ET
BT 34.016 256.577 Td /F1 8.2 Tf [(basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book )] TJ ET
BT 34.016 246.503 Td /F1 8.2 Tf [(proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local )] TJ ET
BT 34.016 236.430 Td /F1 8.2 Tf [(fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y )] TJ ET
BT 34.016 226.357 Td /F1 8.2 Tf [(= X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more )] TJ ET
BT 34.016 216.284 Td /F1 8.2 Tf [(advanced topics.)] TJ ET
BT 34.016 206.210 Td /F1 8.2 Tf [(The Arithmetic of Dynamical Systems)] TJ ET
BT 171.089 206.210 Td /F1 8.2 Tf [( J.H. Silverman 2010-05-05 This book provides an introduction to the relatively new discipline of arithmetic )] TJ ET
BT 34.016 196.137 Td /F1 8.2 Tf [(dynamics. Whereas classical discrete dynamics is the study of iteration of self-maps of the complex plane or real line, arithmetic dynamics is )] TJ ET
BT 34.016 186.064 Td /F1 8.2 Tf [(the study of the number-theoretic properties of rational and algebraic points under repeated application of a polynomial or rational function. A )] TJ ET
BT 34.016 175.991 Td /F1 8.2 Tf [(principal theme of arithmetic dynamics is that many of the fundamental problems in the theory of Diophantine equations have dynamical )] TJ ET
BT 34.016 165.917 Td /F1 8.2 Tf [(analogs.This graduate-level text provides an entry for students into an active field of research and serves as a standard reference for )] TJ ET
BT 34.016 155.844 Td /F1 8.2 Tf [(researchers.)] TJ ET
BT 34.016 145.771 Td /F1 8.2 Tf [(The Arithmetic of Polynomial Dynamical Pairs)] TJ ET
BT 200.888 145.771 Td /F1 8.2 Tf [( Charles Favre 2022-06-14 New mathematical research in arithmetic dynamics In The Arithmetic )] TJ ET
BT 34.016 135.698 Td /F1 8.2 Tf [(of Polynomial Dynamical Pairs, Charles Favre and Thomas Gauthier present new mathematical research in the field of arithmetic dynamics. )] TJ ET
BT 34.016 125.624 Td /F1 8.2 Tf [(Specifically, the authors study one-dimensional algebraic families of pairs given by a polynomial with a marked point. Combining tools from )] TJ ET
BT 34.016 115.551 Td /F1 8.2 Tf [(arithmetic geometry and holomorphic dynamics, they prove an “unlikely intersection” statement for such pairs, thereby demonstrating strong )] TJ ET
BT 34.016 105.478 Td /F1 8.2 Tf [(rigidity features for them. They further describe one-dimensional families in the moduli space of polynomials containing infinitely many )] TJ ET
BT 34.016 95.405 Td /F1 8.2 Tf [(postcritically finite parameters, proving the dynamical André-Oort conjecture for curves in this context, originally stated by Baker and DeMarco. )] TJ ET
BT 34.016 85.331 Td /F1 8.2 Tf [(This is a reader-friendly invitation to a new and exciting research area that brings together sophisticated tools from many branches of )] TJ ET
BT 34.016 75.258 Td /F1 8.2 Tf [(mathematics.)] TJ ET
BT 34.016 65.185 Td /F1 8.2 Tf [(Applied Algebraic Dynamics)] TJ ET
BT 136.712 65.185 Td /F1 8.2 Tf [( Vladimir Anashin 2009 This monograph presents recent developments of the theory of algebraic dynamical )] TJ ET
BT 34.016 55.112 Td /F1 8.2 Tf [(systems and their applications to computer sciences, cryptography, cognitive sciences, psychology, image analysis, and numerical simulations. )] TJ ET
BT 34.016 45.038 Td /F1 8.2 Tf [(The most important mathematical results presented in this book are in the fields of ergodicity, p-adic numbers, and noncommutative groups. For )] TJ ET
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BT 34.016 377.456 Td /F1 8.2 Tf [(students and researchers working on the theory of dynamical systems, algebra, number theory, measure theory, computer sciences, )] TJ ET
BT 34.016 367.382 Td /F1 8.2 Tf [(cryptography, and image analysis.)] TJ ET
BT 34.016 357.309 Td /F1 8.2 Tf [(Women in Numbers Europe II)] TJ ET
BT 142.676 357.309 Td /F1 8.2 Tf [( Irene I. Bouw 2018-06-01 Inspired by the September 2016 conference of the same name, this second volume )] TJ ET
BT 34.016 347.236 Td /F1 8.2 Tf [(highlights recent research in a wide range of topics in contemporary number theory and arithmetic geometry. Research reports from projects )] TJ ET
BT 34.016 337.163 Td /F1 8.2 Tf [(started at the conference, expository papers describing ongoing research, and contributed papers from women number theorists outside the )] TJ ET
BT 34.016 327.089 Td /F1 8.2 Tf [(conference make up this diverse volume. Topics cover a broad range of topics such as arithmetic dynamics, failure of local-global principles, )] TJ ET
BT 34.016 317.016 Td /F1 8.2 Tf [(geometry in positive characteristics, and heights of algebraic integers. The use of tools from algebra, analysis and geometry, as well as )] TJ ET
BT 34.016 306.943 Td /F1 8.2 Tf [(computational methods exemplifies the wealth of techniques available to modern researchers in number theory. Exploring connections between )] TJ ET
BT 34.016 296.870 Td /F1 8.2 Tf [(different branches of mathematics and combining different points of view, these papers continue the tradition of supporting and highlighting the )] TJ ET
BT 34.016 286.796 Td /F1 8.2 Tf [(contributions of women number theorists at a variety of career stages. Perfect for students and researchers interested in the field, this volume )] TJ ET
BT 34.016 276.723 Td /F1 8.2 Tf [(provides an easily accessible introduction and has the potential to inspire future work.)] TJ ET
BT 34.016 266.650 Td /F1 8.2 Tf [(Mathematics of Complexity and Dynamical Systems)] TJ ET
0.165 w 0 J [ ] 0 d
34.016 265.289 m 223.815 265.289 l S
BT 223.815 266.650 Td /F1 8.2 Tf [( Robert A. Meyers 2011-10-05 Mathematics of Complexity and Dynamical Systems is an )] TJ ET
BT 34.016 256.577 Td /F1 8.2 Tf [(authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and )] TJ ET
BT 34.016 246.503 Td /F1 8.2 Tf [(applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective )] TJ ET
BT 34.016 236.430 Td /F1 8.2 Tf [(behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often )] TJ ET
BT 34.016 226.357 Td /F1 8.2 Tf [(characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely )] TJ ET
BT 34.016 216.284 Td /F1 8.2 Tf [(deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and )] TJ ET
BT 34.016 206.210 Td /F1 8.2 Tf [(applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, )] TJ ET
BT 34.016 196.137 Td /F1 8.2 Tf [(systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those )] TJ ET
BT 34.016 186.064 Td /F1 8.2 Tf [(interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.)] TJ ET
BT 34.016 175.991 Td /F1 8.2 Tf [(Handbook of Teichmüller Theory)] TJ ET
0.165 w 0 J [ ] 0 d
34.016 174.629 m 153.682 174.629 l S
BT 153.682 175.991 Td /F1 8.2 Tf [( Athanase Papadopoulos 2007 )] TJ ET
BT 34.016 165.917 Td /F1 8.2 Tf [(Number Theory Revealed: A Masterclass)] TJ ET
0.165 w 0 J [ ] 0 d
34.016 164.556 m 184.850 164.556 l S
BT 184.850 165.917 Td /F1 8.2 Tf [( Andrew Granville 2020-09-23 Number Theory Revealed: A Masterclass acquaints enthusiastic )] TJ ET
BT 34.016 155.844 Td /F1 8.2 Tf [(students with the “Queen of Mathematics”. The text offers a fresh take on congruences, power residues, quadratic residues, primes, and )] TJ ET
BT 34.016 145.771 Td /F1 8.2 Tf [(Diophantine equations and presents hot topics like cryptography, factoring, and primality testing. Students are also introduced to beautiful )] TJ ET
BT 34.016 135.698 Td /F1 8.2 Tf [(enlightening questions like the structure of Pascal's triangle mod $p$ and modern twists on traditional questions like the values represented by )] TJ ET
BT 34.016 125.624 Td /F1 8.2 Tf [(binary quadratic forms, the anatomy of integers, and elliptic curves. This Masterclass edition contains many additional chapters and appendices )] TJ ET
BT 34.016 115.551 Td /F1 8.2 Tf [(not found in Number Theory Revealed: An Introduction, highlighting beautiful developments and inspiring other subjects in mathematics \(like )] TJ ET
BT 34.016 105.478 Td /F1 8.2 Tf [(algebra\). This allows instructors to tailor a course suited to their own \(and their students'\) interests. There are new yet accessible topics like the )] TJ ET
BT 34.016 95.405 Td /F1 8.2 Tf [(curvature of circles in a tiling of a circle by circles, the latest discoveries on gaps between primes, a new proof of Mordell's Theorem for )] TJ ET
BT 34.016 85.331 Td /F1 8.2 Tf [(congruent elliptic curves, and a discussion of the $abc$-conjecture including its proof for polynomials. About the Author: Andrew Granville is the )] TJ ET
BT 34.016 75.258 Td /F1 8.2 Tf [(Canada Research Chair in Number Theory at the University of Montreal and professor of mathematics at University College London. He has )] TJ ET
BT 34.016 65.185 Td /F1 8.2 Tf [(won several international writing prizes for exposition in mathematics, including the 2008 Chauvenet Prize and the 2019 Halmos-Ford Prize, )] TJ ET
BT 34.016 55.112 Td /F1 8.2 Tf [(and is the author of Prime Suspects \(Princeton University Press, 2019\), a beautifully illustrated graphic novel murder mystery that explores )] TJ ET
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BT 34.016 377.456 Td /F1 8.2 Tf [(surprising connections between the anatomies of integers and of permutations.)] TJ ET
BT 34.016 367.382 Td /F1 8.2 Tf [(Dynamical Systems, Number Theory and Applications)] TJ ET
BT 231.158 367.382 Td /F1 8.2 Tf [( Thomas Hagen 2016-01-25 This volume consists of a selection of research-type articles )] TJ ET
BT 34.016 357.309 Td /F1 8.2 Tf [(on dynamical systems, evolution equations, analytic number theory and closely related topics. A strong emphasis is on a fair balance between )] TJ ET
BT 34.016 347.236 Td /F1 8.2 Tf [(theoretical and more applied work, thus spanning the chasm between abstract insight and actual application. Several of the articles are )] TJ ET
BT 34.016 337.163 Td /F1 8.2 Tf [(expected to be in the intersection of dynamical systems theory and number theory. One article will likely relate the topics presented to the )] TJ ET
BT 34.016 327.089 Td /F1 8.2 Tf [(academic achievements and interests of Prof. Leutbecher and shed light on common threads among all the contributions. )] TJ ET
BT 34.016 317.016 Td /F1 8.2 Tf [(Contents:PrefaceBiographical Note on Armin Leutbecher \(S Walcher\)Das Jahr 1934 ... \(J Fischer\)Explicit Expressions for Equivariant Minimal )] TJ ET
BT 34.016 306.943 Td /F1 8.2 Tf [(Lagrangian Surfaces \(J F Dorfmeister & H Ma\)Rational Parameter Rays of the Multibrot Sets \(D Eberlein, S Mukherjee & D Schleicher\)The )] TJ ET
BT 34.016 296.870 Td /F1 8.2 Tf [(Matovich-Pearson Equations Revisited \(T Hagen\)Diffeomorphisms with Stable Manifolds as Basin Boundaries \(S Hayes & Ch Wolf\)A New Type )] TJ ET
BT 34.016 286.796 Td /F1 8.2 Tf [(of Functional Equations of Euler Products \(B Heim\)The Hexagonal Lattice and the Epstein Zeta Function \(A Henn\)On Putative q-Analogues of )] TJ ET
BT 34.016 276.723 Td /F1 8.2 Tf [(the Fano Plane \(Th Honold & M Kiermaier\)Integral Orthogonal Groups \(A Krieg\)The Role of Fourier Analysis in X-Ray Crystallography \(F Rupp )] TJ ET
BT 34.016 266.650 Td /F1 8.2 Tf [(& J Scheurle\)An Elementary Proof for Joint Continuity of Semiflows \(S Schmitz\)A Convergent String Method \(H Schwetlick & J )] TJ ET
BT 34.016 256.577 Td /F1 8.2 Tf [(Zimmer\)Variational Symmetries and Pluri-Lagrangian Systems \(Y B Suris\) Readership: Researchers in algebra and number theory, dynamical )] TJ ET
BT 34.016 246.503 Td /F1 8.2 Tf [(systems and analysis and differential equations. Key Features:This versatile book covers state-of-the art work in dynamical systems, analytic )] TJ ET
BT 34.016 236.430 Td /F1 8.2 Tf [(number theory and applied analysisIt appeals to a wide audience due to its broad range of topics, highlighting both the breadth and the depth of )] TJ ET
BT 34.016 226.357 Td /F1 8.2 Tf [(modern analytical work without losing sight of a common coreKeywords:Dynamical Systems;Evolution Equations;Number Theory;Differential )] TJ ET
BT 34.016 216.284 Td /F1 8.2 Tf [(Geometry)] TJ ET
BT 34.016 206.210 Td /F1 8.2 Tf [(Research Directions in Number Theory)] TJ ET
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BT 176.592 206.210 Td /F1 8.2 Tf [( Jennifer S. Balakrishnan 2019-08-01 These proceedings collect several number theory articles, most of )] TJ ET
BT 34.016 196.137 Td /F1 8.2 Tf [(which were written in connection to the workshop WIN4: Women in Numbers, held in August 2017, at the Banff International Research Station )] TJ ET
BT 34.016 186.064 Td /F1 8.2 Tf [(\(BIRS\) in Banff, Alberta, Canada. It collects papers disseminating research outcomes from collaborations initiated during the workshop as well )] TJ ET
BT 34.016 175.991 Td /F1 8.2 Tf [(as other original research contributions involving participants of the WIN workshops. The workshop and this volume are part of the WIN )] TJ ET
BT 34.016 165.917 Td /F1 8.2 Tf [(network, aimed at highlighting the research of women and gender minorities in number theory as well as increasing their participation and )] TJ ET
BT 34.016 155.844 Td /F1 8.2 Tf [(boosting their potential collaborations in number theory and related fields.)] TJ ET
BT 34.016 145.771 Td /F1 8.2 Tf [(Dynamical Systems)] TJ ET
BT 106.442 145.771 Td /F1 8.2 Tf [( George David Birkhoff 2018-11-10 This work has been selected by scholars as being culturally important and is part of the )] TJ ET
BT 34.016 135.698 Td /F1 8.2 Tf [(knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. )] TJ ET
BT 34.016 125.624 Td /F1 8.2 Tf [(Within the United States, you may freely copy and distribute this work, as no entity \(individual or corporate\) has a copyright on the body of the )] TJ ET
BT 34.016 115.551 Td /F1 8.2 Tf [(work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the )] TJ ET
BT 34.016 105.478 Td /F1 8.2 Tf [(public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original )] TJ ET
BT 34.016 95.405 Td /F1 8.2 Tf [(graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an )] TJ ET
BT 34.016 85.331 Td /F1 8.2 Tf [(important part of keeping this knowledge alive and relevant.)] TJ ET
BT 34.016 75.258 Td /F1 8.2 Tf [(Advances in Non-Archimedean Analysis)] TJ ET
BT 180.734 75.258 Td /F1 8.2 Tf [( Helge Glöckner 2016-05-20 This volume contains the Proceedings of the 13th International )] TJ ET
BT 34.016 65.185 Td /F1 8.2 Tf [(Conference on p-adic Functional Analysis, held from August 12–16, 2014, at the University of Paderborn, Paderborn, Germany. The articles )] TJ ET
BT 34.016 55.112 Td /F1 8.2 Tf [(included in this book feature recent developments in various areas of non-Archimedean analysis, non-Archimedean functional analysis, )] TJ ET
BT 34.016 45.038 Td /F1 8.2 Tf [(representation theory, number theory, non-Archimedean dynamical systems and applications. Through a combination of new research articles )] TJ ET
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BT 34.016 377.456 Td /F1 8.2 Tf [(and survey papers, this book provides the reader with an overview of current developments and techniques in non-Archimedean analysis as )] TJ ET
BT 34.016 367.382 Td /F1 8.2 Tf [(well as a broad knowledge of some of the sub-areas of this exciting and fast-developing research area.)] TJ ET
BT 34.016 357.309 Td /F1 8.2 Tf [(The Dynamical Mordell–Lang Conjecture)] TJ ET
BT 183.481 357.309 Td /F1 8.2 Tf [( Jason P. Bell 2016-04-20 The Dynamical Mordell-Lang Conjecture is an analogue of the classical )] TJ ET
BT 34.016 347.236 Td /F1 8.2 Tf [(Mordell-Lang conjecture in the context of arithmetic dynamics. It predicts the behavior of the orbit of a point x under the action of an )] TJ ET
BT 34.016 337.163 Td /F1 8.2 Tf [(endomorphism f of a quasiprojective complex variety X. More precisely, it claims that for any point x in X and any subvariety V of X, the set of )] TJ ET
BT 34.016 327.089 Td /F1 8.2 Tf [(indices n such that the n-th iterate of x under f lies in V is a finite union of arithmetic progressions. In this book the authors present all known )] TJ ET
BT 34.016 317.016 Td /F1 8.2 Tf [(results about the Dynamical Mordell-Lang Conjecture, focusing mainly on a p-adic approach which provides a parametrization of the orbit of a )] TJ ET
BT 34.016 306.943 Td /F1 8.2 Tf [(point under an endomorphism of a variety.)] TJ ET
BT 34.016 296.870 Td /F1 8.2 Tf [(Dynamical Systems and Ergodic Theory)] TJ ET
BT 180.725 296.870 Td /F1 8.2 Tf [( Mark Pollicott 1998-01-29 Essentially a self-contained text giving an introduction to topological )] TJ ET
BT 34.016 286.796 Td /F1 8.2 Tf [(dynamics and ergodic theory.)] TJ ET
BT 34.016 276.723 Td /F1 8.2 Tf [(Berkovich Spaces and Applications)] TJ ET
BT 162.864 276.723 Td /F1 8.2 Tf [( Antoine Ducros 2014-11-21 We present an introduction to Berkovich’s theory of non-archimedean analytic )] TJ ET
BT 34.016 266.650 Td /F1 8.2 Tf [(spaces that emphasizes its applications in various fields. The first part contains surveys of a foundational nature, including an introduction to )] TJ ET
BT 34.016 256.577 Td /F1 8.2 Tf [(Berkovich analytic spaces by M. Temkin, and to étale cohomology by A. Ducros, as well as a short note by C. Favre on the topology of some )] TJ ET
BT 34.016 246.503 Td /F1 8.2 Tf [(Berkovich spaces. The second part focuses on applications to geometry. A second text by A. Ducros contains a new proof of the fact that the )] TJ ET
BT 34.016 236.430 Td /F1 8.2 Tf [(higher direct images of a coherent sheaf under a proper map are coherent, and B. Rémy, A. Thuillier and A. Werner provide an overview of )] TJ ET
BT 34.016 226.357 Td /F1 8.2 Tf [(their work on the compactification of Bruhat-Tits buildings using Berkovich analytic geometry. The third and final part explores the relationship )] TJ ET
BT 34.016 216.284 Td /F1 8.2 Tf [(between non-archimedean geometry and dynamics. A contribution by M. Jonsson contains a thorough discussion of non-archimedean )] TJ ET
BT 34.016 206.210 Td /F1 8.2 Tf [(dynamical systems in dimension 1 and 2. Finally a survey by J.-P. Otal gives an account of Morgan-Shalen's theory of compactification of )] TJ ET
BT 34.016 196.137 Td /F1 8.2 Tf [(character varieties. This book will provide the reader with enough material on the basic concepts and constructions related to Berkovich spaces )] TJ ET
BT 34.016 186.064 Td /F1 8.2 Tf [(to move on to more advanced research articles on the subject. We also hope that the applications presented here will inspire the reader to )] TJ ET
BT 34.016 175.991 Td /F1 8.2 Tf [(discover new settings where these beautiful and intricate objects might arise.)] TJ ET
BT 34.016 165.917 Td /F1 8.2 Tf [(The Arithmetic of Elliptic Curves)] TJ ET
BT 150.918 165.917 Td /F1 8.2 Tf [( Joseph H. Silverman 2010-11-19 The theory of elliptic curves is distinguished by its long history and by the )] TJ ET
BT 34.016 155.844 Td /F1 8.2 Tf [(diversity of the methods that have been used in its study. This book treats the arithmetic approach in its modern formulation, through the use of )] TJ ET
BT 34.016 145.771 Td /F1 8.2 Tf [(basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book )] TJ ET
BT 34.016 135.698 Td /F1 8.2 Tf [(proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local )] TJ ET
BT 34.016 125.624 Td /F1 8.2 Tf [(fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y )] TJ ET
BT 34.016 115.551 Td /F1 8.2 Tf [(= X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more )] TJ ET
BT 34.016 105.478 Td /F1 8.2 Tf [(advanced topics.)] TJ ET
BT 34.016 95.405 Td /F1 8.2 Tf [(Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics: Fractals in pure mathematics)] TJ ET
BT 422.351 95.405 Td /F1 8.2 Tf [( David Carfi 2013-10-22 This volume )] TJ ET
BT 34.016 85.331 Td /F1 8.2 Tf [(contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical )] TJ ET
BT 34.016 75.258 Td /F1 8.2 Tf [(Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied )] TJ ET
BT 34.016 65.185 Td /F1 8.2 Tf [(Mathematics, in memory of Benoit Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and )] TJ ET
BT 34.016 55.112 Td /F1 8.2 Tf [(Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry \(and some aspects of )] TJ ET
BT 34.016 45.038 Td /F1 8.2 Tf [(dynamical systems\) in pure mathematics. Also included are articles discussing a variety of connections of fractal geometry with other fields of )] TJ ET
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BT 34.016 377.456 Td /F1 8.2 Tf [(mathematics, including probability theory, number theory, geometric measure theory, partial differential equations, global analysis on non-)] TJ ET
BT 34.016 367.382 Td /F1 8.2 Tf [(smooth spaces, harmonic analysis and spectral geometry. The companion volume \(Contemporary Mathematics, Volume 601\) focuses on )] TJ ET
BT 34.016 357.309 Td /F1 8.2 Tf [(applications of fractal geometry and dynamical systems to other sciences, including physics, engineering, computer science, economics, and )] TJ ET
BT 34.016 347.236 Td /F1 8.2 Tf [(finance.)] TJ ET
BT 34.016 337.163 Td /F1 8.2 Tf [(Ergodic Theory, Dynamical Systems, and the Continuing Influence of John C. Oxtoby)] TJ ET
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BT 344.900 337.163 Td /F1 8.2 Tf [( Joseph Auslander 2016-11-29 This volume contains the )] TJ ET
BT 34.016 327.089 Td /F1 8.2 Tf [(proceedings of three conferences in Ergodic Theory and Symbolic Dynamics: the Oxtoby Centennial Conference, held from October 30–31, )] TJ ET
BT 34.016 317.016 Td /F1 8.2 Tf [(2010, at Bryn Mawr College; the Williams Ergodic Theory Conference, held from July 27–29, 2012, at Williams College; and the AMS Special )] TJ ET
BT 34.016 306.943 Td /F1 8.2 Tf [(Session on Ergodic Theory and Symbolic Dynamics, held from January 17–18, 2014, in Baltimore, MD. This volume contains articles covering a )] TJ ET
BT 34.016 296.870 Td /F1 8.2 Tf [(variety of topics in measurable, symbolic and complex dynamics. It also includes a survey article on the life and work of John Oxtoby, providing )] TJ ET
BT 34.016 286.796 Td /F1 8.2 Tf [(a source of information about the many ways Oxtoby's work influenced mathematical thought in this and other fields.)] TJ ET
BT 36.266 256.567 Td /F1 8.0 Tf [(the-arithmetic-of-dynamical-systems-graduate-texts-in-mathematics-241-)] TJ ET
BT 36.266 246.799 Td /F1 8.0 Tf [(by-silverman-joseph-h-author-jun-06-2007-hardcover)] TJ ET
BT 323.350 251.891 Td /F1 8.0 Tf [(Downloaded from )] TJ ET
BT 388.262 251.683 Td /F1 8.0 Tf [(diagramiq.com)] TJ ET
BT 440.718 251.891 Td /F1 8.0 Tf [( on September 28, 2022 by guest)] TJ ET
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