Topics In Dynamics And Ergodic Theory

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Topics in Dynamics and Ergodic Theory

Sergey Bezuglyi
Topics in Dynamics and Ergodic Theory Book PDF

Author : Sergey Bezuglyi
Publisher : Cambridge University Press
Page : 276 pages
File Size : 44,7 Mb
Release : 2003-12-08
Category : Mathematics
ISBN : 0521533651

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Topics in Dynamics and Ergodic Theory by Sergey Bezuglyi Pdf

This book contains a collection of survey papers by leading researchers in ergodic theory, low-dimensional and topological dynamics and it comprises nine chapters on a range of important topics. These include: the role and usefulness of ultrafilters in ergodic theory, topological dynamics and Ramsey theory; topological aspects of kneading theory together with an analogous 2-dimensional theory called pruning; the dynamics of Markov odometers, Bratteli-Vershik diagrams and orbit equivalence of non-singular automorphisms; geometric proofs of Mather's connecting and accelerating theorems; recent results in one dimensional smooth dynamics; periodic points of nonexpansive maps; arithmetic dynamics; the defect of factor maps; entropy theory for actions of countable amenable groups.

Ergodic Theory and Dynamical Systems

Yves Coudène
Ergodic Theory and Dynamical Systems Book PDF

Author : Yves Coudène
Publisher : Springer
Page : 190 pages
File Size : 49,5 Mb
Release : 2016-11-10
Category : Mathematics
ISBN : 9781447172871

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Ergodic Theory and Dynamical Systems by Yves Coudène Pdf

This textbook is a self-contained and easy-to-read introduction to ergodic theory and the theory of dynamical systems, with a particular emphasis on chaotic dynamics. This book contains a broad selection of topics and explores the fundamental ideas of the subject. Starting with basic notions such as ergodicity, mixing, and isomorphisms of dynamical systems, the book then focuses on several chaotic transformations with hyperbolic dynamics, before moving on to topics such as entropy, information theory, ergodic decomposition and measurable partitions. Detailed explanations are accompanied by numerous examples, including interval maps, Bernoulli shifts, toral endomorphisms, geodesic flow on negatively curved manifolds, Morse-Smale systems, rational maps on the Riemann sphere and strange attractors. Ergodic Theory and Dynamical Systems will appeal to graduate students as well as researchers looking for an introduction to the subject. While gentle on the beginning student, the book also contains a number of comments for the more advanced reader.

Ergodic Dynamics

Jane Hawkins
Ergodic Dynamics Book PDF

Author : Jane Hawkins
Publisher : Springer Nature
Page : 340 pages
File Size : 48,5 Mb
Release : 2021-01-28
Category : Mathematics
ISBN : 9783030592424

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Ergodic Dynamics by Jane Hawkins Pdf

This textbook provides a broad introduction to the fields of dynamical systems and ergodic theory. Motivated by examples throughout, the author offers readers an approachable entry-point to the dynamics of ergodic systems. Modern and classical applications complement the theory on topics ranging from financial fraud to virus dynamics, offering numerous avenues for further inquiry. Starting with several simple examples of dynamical systems, the book begins by establishing the basics of measurable dynamical systems, attractors, and the ergodic theorems. From here, chapters are modular and can be selected according to interest. Highlights include the Perron–Frobenius theorem, which is presented with proof and applications that include Google PageRank. An in-depth exploration of invariant measures includes ratio sets and type III measurable dynamical systems using the von Neumann factor classification. Topological and measure theoretic entropy are illustrated and compared in detail, with an algorithmic application of entropy used to study the papillomavirus genome. A chapter on complex dynamics introduces Julia sets and proves their ergodicity for certain maps. Cellular automata are explored as a series of case studies in one and two dimensions, including Conway’s Game of Life and latent infections of HIV. Other chapters discuss mixing properties, shift spaces, and toral automorphisms. Ergodic Dynamics unifies topics across ergodic theory, topological dynamics, complex dynamics, and dynamical systems, offering an accessible introduction to the area. Readers across pure and applied mathematics will appreciate the rich illustration of the theory through examples, real-world connections, and vivid color graphics. A solid grounding in measure theory, topology, and complex analysis is assumed; appendices provide a brief review of the essentials from measure theory, functional analysis, and probability.

Topics in Ergodic Theory

William Parry
Topics in Ergodic Theory Book PDF

Author : William Parry
Publisher : Cambridge University Press
Page : 128 pages
File Size : 49,5 Mb
Release : 2004-06-03
Category : Mathematics
ISBN : 0521604907

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Topics in Ergodic Theory by William Parry Pdf

An introduction to topics and examples of ergodic theory, a central area of pure mathematics.

Ergodic Theory

Manfred Einsiedler,Thomas Ward
Ergodic Theory Book PDF

Author : Manfred Einsiedler,Thomas Ward
Publisher : Springer Science & Business Media
Page : 481 pages
File Size : 48,5 Mb
Release : 2010-09-11
Category : Mathematics
ISBN : 9780857290212

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Ergodic Theory by Manfred Einsiedler,Thomas Ward Pdf

This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence. Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl's polynomial equidistribution theorem, the ergodic proof of Szemeredi's theorem, the connection between the continued fraction map and the modular surface, and a proof of the equidistribution of horocycle orbits. Ergodic Theory with a view towards Number Theory will appeal to mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory, homogenous dynamics or number theory.

Topics in Ergodic Theory (PMS-44), Volume 44

Iakov Grigorevich Sinai
Topics in Ergodic Theory PMS 44 Volume 44 Book PDF

Author : Iakov Grigorevich Sinai
Publisher : Princeton University Press
Page : 226 pages
File Size : 45,6 Mb
Release : 2017-03-14
Category : Mathematics
ISBN : 9781400887255

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Topics in Ergodic Theory (PMS-44), Volume 44 by Iakov Grigorevich Sinai Pdf

This book concerns areas of ergodic theory that are now being intensively developed. The topics include entropy theory (with emphasis on dynamical systems with multi-dimensional time), elements of the renormalization group method in the theory of dynamical systems, splitting of separatrices, and some problems related to the theory of hyperbolic dynamical systems. Originally published in 1993. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Ergodic Theory and Differentiable Dynamics

Ricardo Mañé
Ergodic Theory and Differentiable Dynamics Book PDF

Author : Ricardo Mañé
Publisher : Springer Science & Business Media
Page : 317 pages
File Size : 52,6 Mb
Release : 1987-01
Category : Entropia
ISBN : 3540152784

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Ergodic Theory and Differentiable Dynamics by Ricardo Mañé Pdf

This version differs from the Portuguese edition only in a few additions and many minor corrections. Naturally, this edition raised the question of whether to use the opportunity to introduce major additions. In a book like this, ending in the heart of a rich research field, there are always further topics that should arguably be included. Subjects like geodesic flows or the role of Hausdorff dimension in con­ temporary ergodic theory are two of the most tempting gaps to fill. However, I let it stand with practically the same boundaries as the original version, still believing these adequately fulfill its goal of presenting the basic knowledge required to approach the research area of Differentiable Ergodic Theory. I wish to thank Dr. Levy for the excellent translation and several of the correc­ tions mentioned above. Rio de Janeiro, January 1987 Ricardo Mane Introduction This book is an introduction to ergodic theory, with emphasis on its relationship with the theory of differentiable dynamical systems, which is sometimes called differentiable ergodic theory. Chapter 0, a quick review of measure theory, is included as a reference. Proofs are omitted, except for some results on derivatives with respect to sequences of partitions, which are not generally found in standard texts on measure and integration theory and tend to be lost within a much wider framework in more advanced texts.

Ergodic Theory and Differentiable Dynamics

Ricardo Mane
Ergodic Theory and Differentiable Dynamics Book PDF

Author : Ricardo Mane
Publisher : Springer Science & Business Media
Page : 328 pages
File Size : 41,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642703355

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Ergodic Theory and Differentiable Dynamics by Ricardo Mane Pdf

This version differs from the Portuguese edition only in a few additions and many minor corrections. Naturally, this edition raised the question of whether to use the opportunity to introduce major additions. In a book like this, ending in the heart of a rich research field, there are always further topics that should arguably be included. Subjects like geodesic flows or the role of Hausdorff dimension in con temporary ergodic theory are two of the most tempting gaps to fill. However, I let it stand with practically the same boundaries as the original version, still believing these adequately fulfill its goal of presenting the basic knowledge required to approach the research area of Differentiable Ergodic Theory. I wish to thank Dr. Levy for the excellent translation and several of the correc tions mentioned above. Rio de Janeiro, January 1987 Ricardo Mane Introduction This book is an introduction to ergodic theory, with emphasis on its relationship with the theory of differentiable dynamical systems, which is sometimes called differentiable ergodic theory. Chapter 0, a quick review of measure theory, is included as a reference. Proofs are omitted, except for some results on derivatives with respect to sequences of partitions, which are not generally found in standard texts on measure and integration theory and tend to be lost within a much wider framework in more advanced texts.

Topics in Ergodic Theory (PMS-44), Volume 44

Iakov Grigorevich Sinai
Topics in Ergodic Theory PMS 44 Volume 44 Book PDF

Author : Iakov Grigorevich Sinai
Publisher : Unknown
Page : 0 pages
File Size : 50,7 Mb
Release : 2017-03-21
Category : Ergodic theory
ISBN : 0691628319

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Topics in Ergodic Theory (PMS-44), Volume 44 by Iakov Grigorevich Sinai Pdf

This book concerns areas of ergodic theory that are now being intensively developed. The topics include entropy theory (with emphasis on dynamical systems with multi-dimensional time), elements of the renormalization group method in the theory of dynamical systems, splitting of separatrices, and some problems related to the theory of hyperbolic dynamical systems. Originally published in 1993. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Dynamics, Ergodic Theory and Geometry

Boris Hasselblatt
Dynamics Ergodic Theory and Geometry Book PDF

Author : Boris Hasselblatt
Publisher : Cambridge University Press
Page : 324 pages
File Size : 43,6 Mb
Release : 2007-09-24
Category : Mathematics
ISBN : 9780521875417

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Dynamics, Ergodic Theory and Geometry by Boris Hasselblatt Pdf

Based on the subjects from the Clay Mathematics Institute/Mathematical Sciences Research Institute Workshop titled 'Recent Progress in Dynamics' in September and October 2004, this volume contains surveys and research articles by leading experts in several areas of dynamical systems that have experienced substantial progress. One of the major surveys is on symplectic geometry, which is closely related to classical mechanics and an exciting addition to modern geometry. The survey on local rigidity of group actions gives a broad and up-to-date account of another flourishing subject. Other papers cover hyperbolic, parabolic, and symbolic dynamics as well as ergodic theory. Students and researchers in dynamical systems, geometry, and related areas will find this book fascinating. The book also includes a fifty-page commented problem list that takes the reader beyond the areas covered by the surveys, to inspire and guide further research.

Topics in Dynamics and Ergodic Theory

Sergey Bezuglyi,S. F. Koli︠a︡da
Topics in Dynamics and Ergodic Theory Book PDF

Author : Sergey Bezuglyi,S. F. Koli︠a︡da
Publisher : Unknown
Page : 262 pages
File Size : 46,6 Mb
Release : 2003
Category : Electronic books
ISBN : 0511067690

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Topics in Dynamics and Ergodic Theory by Sergey Bezuglyi,S. F. Koli︠a︡da Pdf

This book contains a collection of survey papers by leading researchers in ergodic theory, low-dimensional and topological dynamics and it comprises nine chapters on a range of important topics.

Ergodic Theory, Hyperbolic Dynamics and Dimension Theory

Luís Barreira
Ergodic Theory Hyperbolic Dynamics and Dimension Theory Book PDF

Author : Luís Barreira
Publisher : Springer Science & Business Media
Page : 290 pages
File Size : 40,5 Mb
Release : 2012-04-28
Category : Mathematics
ISBN : 9783642280900

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Ergodic Theory, Hyperbolic Dynamics and Dimension Theory by Luís Barreira Pdf

Over the last two decades, the dimension theory of dynamical systems has progressively developed into an independent and extremely active field of research. The main aim of this volume is to offer a unified, self-contained introduction to the interplay of these three main areas of research: ergodic theory, hyperbolic dynamics, and dimension theory. It starts with the basic notions of the first two topics and ends with a sufficiently high-level introduction to the third. Furthermore, it includes an introduction to the thermodynamic formalism, which is an important tool in dimension theory. The volume is primarily intended for graduate students interested in dynamical systems, as well as researchers in other areas who wish to learn about ergodic theory, thermodynamic formalism, or dimension theory of hyperbolic dynamics at an intermediate level in a sufficiently detailed manner. In particular, it can be used as a basis for graduate courses on any of these three subjects. The text can also be used for self-study: it is self-contained, and with the exception of some well-known basic facts from other areas, all statements include detailed proofs.

Ergodic Theory

David Kerr,Hanfeng Li
Ergodic Theory Book PDF

Author : David Kerr,Hanfeng Li
Publisher : Springer
Page : 431 pages
File Size : 51,8 Mb
Release : 2017-02-09
Category : Mathematics
ISBN : 9783319498478

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Ergodic Theory by David Kerr,Hanfeng Li Pdf

This book provides an introduction to the ergodic theory and topological dynamics of actions of countable groups. It is organized around the theme of probabilistic and combinatorial independence, and highlights the complementary roles of the asymptotic and the perturbative in its comprehensive treatment of the core concepts of weak mixing, compactness, entropy, and amenability. The more advanced material includes Popa's cocycle superrigidity, the Furstenberg-Zimmer structure theorem, and sofic entropy. The structure of the book is designed to be flexible enough to serve a variety of readers. The discussion of dynamics is developed from scratch assuming some rudimentary functional analysis, measure theory, and topology, and parts of the text can be used as an introductory course. Researchers in ergodic theory and related areas will also find the book valuable as a reference.

Ergodic Theory

Idris Assani
Ergodic Theory Book PDF

Author : Idris Assani
Publisher : Walter de Gruyter GmbH & Co KG
Page : 148 pages
File Size : 47,8 Mb
Release : 2016-06-20
Category : Mathematics
ISBN : 9783110460919

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Ergodic Theory by Idris Assani Pdf

This monograph discusses recent advances in ergodic theory and dynamical systems. As a mixture of survey papers of active research areas and original research papers, this volume attracts young and senior researchers alike. Contents: Duality of the almost periodic and proximal relations Limit directions of a vector cocycle, remarks and examples Optimal norm approximation in ergodic theory The iterated Prisoner’s Dilemma: good strategies and their dynamics Lyapunov exponents for conservative twisting dynamics: a survey Takens’ embedding theorem with a continuous observable

Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics

Sébastien Ferenczi,Joanna Kułaga-Przymus,Mariusz Lemańczyk
Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics Book PDF

Author : Sébastien Ferenczi,Joanna Kułaga-Przymus,Mariusz Lemańczyk
Publisher : Springer
Page : 434 pages
File Size : 50,9 Mb
Release : 2018-06-15
Category : Mathematics
ISBN : 9783319749082

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Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics by Sébastien Ferenczi,Joanna Kułaga-Przymus,Mariusz Lemańczyk Pdf

This book concentrates on the modern theory of dynamical systems and its interactions with number theory and combinatorics. The greater part begins with a course in analytic number theory and focuses on its links with ergodic theory, presenting an exhaustive account of recent research on Sarnak's conjecture on Möbius disjointness. Selected topics involving more traditional connections between number theory and dynamics are also presented, including equidistribution, homogenous dynamics, and Lagrange and Markov spectra. In addition, some dynamical and number theoretical aspects of aperiodic order, some algebraic systems, and a recent development concerning tame systems are described.