Topics In Ergodic Theory

Author : Iakov Grigorevich Sinai
Publisher : Princeton University Press
Page : 226 pages
File Size : 42,7 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.

Author : William Parry
Publisher : Cambridge University Press
Page : 128 pages
File Size : 53,7 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.

Author : Sergey Bezuglyi
Publisher : Cambridge University Press
Page : 276 pages
File Size : 46,5 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.

Author : Yves Coudène
Publisher : Springer
Page : 190 pages
File Size : 41,6 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.

Author : Manfred Einsiedler,Thomas Ward
Publisher : Springer Science & Business Media
Page : 481 pages
File Size : 50,9 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.

Author : Karma Dajani,Cor Kraaikamp
Publisher : American Mathematical Soc.
Page : 190 pages
File Size : 41,5 Mb
Release : 2002-12-31
Category : Mathematics
ISBN : 9780883850343

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Ergodic Theory of Numbers by Karma Dajani,Cor Kraaikamp Pdf

Ergodic Theory of Numbers looks at the interaction between two fields of mathematics: number theory and ergodic theory (as part of dynamical systems). It is an introduction to the ergodic theory behind common number expansions, like decimal expansions, continued fractions, and many others. However, its aim does not stop there. For undergraduate students with sufficient background knowledge in real analysis and graduate students interested in the area, it is also an introduction to a "dynamical way of thinking". The questions studied here are dynamical as well as number theoretical in nature, and the answers are obtained with the help of ergodic theory. Attention is focused on concepts like measure-preserving, ergodicity, natural extension, induced transformations, and entropy. These concepts are then applied to familiar expansions to obtain old and new results in an elegant and straightforward manner. What it means to be ergodic and the basic ideas behind ergodic theory will be explained along the way. The subjects covered vary from classical to recent, which makes this book appealing to researchers as well as students.

Author : I͡Akov Grigorʹevich Sinaĭ,IA. G. Sinai,I︠A︡kov Grigorʹevich Sinaĭ,Ya. G. Sinai,Ya G. Sinai,Âkov Grigorʹevič Sinaj
Publisher : Unknown
Page : 218 pages
File Size : 51,6 Mb
Release : 1994
Category : Mathematics
ISBN : 0691032777

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Topics in Ergodic Theory by I͡Akov Grigorʹevich Sinaĭ,IA. G. Sinai,I︠A︡kov Grigorʹevich Sinaĭ,Ya. G. Sinai,Ya G. Sinai,Âkov Grigorʹevič Sinaj 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.

Author : Klaus Schmidt
Publisher : American Mathematical Soc.
Page : 102 pages
File Size : 40,9 Mb
Release : 1990
Category : Mathematics
ISBN : 9780821807279

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Algebraic Ideas in Ergodic Theory by Klaus Schmidt Pdf

The author examines the influence of operator algebras on dynamics, concentrating on ergodic equivalence relations. He also covers higher dimensional Markov shifts, making the assumption that the Markov shift carries a group structure.

Author : Karl E. Petersen
Publisher : Cambridge University Press
Page : 452 pages
File Size : 49,9 Mb
Release : 1995-01-27
Category : Mathematics
ISBN : 9780521459990

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Ergodic Theory and Harmonic Analysis by Karl E. Petersen Pdf

Ergodic theory is a field that is stimulating on its own, and also in its interactions with other branches of mathematics and science. In recent years, the interchanges with harmonic analysis have been especially noticeable and productive. This book contains survey papers describing the relationship of ergodic theory with convergence, rigidity theory and the theory of joinings. These papers present the background of each area of interaction, the most outstanding results and promising lines of research. They should form perfect starting points for anyone beginning research in one of these areas. Thirteen related research papers describe the work; several treat questions arising from the Furstenberg multiple recurrence theory, while the remainder deal with convergence and a variety of other topics in dynamics.

Author : Tanja Eisner,Bálint Farkas,Markus Haase,Rainer Nagel
Publisher : Springer
Page : 628 pages
File Size : 55,5 Mb
Release : 2015-11-18
Category : Mathematics
ISBN : 9783319168982

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Operator Theoretic Aspects of Ergodic Theory by Tanja Eisner,Bálint Farkas,Markus Haase,Rainer Nagel Pdf

Stunning recent results by Host–Kra, Green–Tao, and others, highlight the timeliness of this systematic introduction to classical ergodic theory using the tools of operator theory. Assuming no prior exposure to ergodic theory, this book provides a modern foundation for introductory courses on ergodic theory, especially for students or researchers with an interest in functional analysis. While basic analytic notions and results are reviewed in several appendices, more advanced operator theoretic topics are developed in detail, even beyond their immediate connection with ergodic theory. As a consequence, the book is also suitable for advanced or special-topic courses on functional analysis with applications to ergodic theory. Topics include: • an intuitive introduction to ergodic theory • an introduction to the basic notions, constructions, and standard examples of topological dynamical systems • Koopman operators, Banach lattices, lattice and algebra homomorphisms, and the Gelfand–Naimark theorem • measure-preserving dynamical systems • von Neumann’s Mean Ergodic Theorem and Birkhoff’s Pointwise Ergodic Theorem • strongly and weakly mixing systems • an examination of notions of isomorphism for measure-preserving systems • Markov operators, and the related concept of a factor of a measure preserving system • compact groups and semigroups, and a powerful tool in their study, the Jacobs–de Leeuw–Glicksberg decomposition • an introduction to the spectral theory of dynamical systems, the theorems of Furstenberg and Weiss on multiple recurrence, and applications of dynamical systems to combinatorics (theorems of van der Waerden, Gallai,and Hindman, Furstenberg’s Correspondence Principle, theorems of Roth and Furstenberg–Sárközy) Beyond its use in the classroom, Operator Theoretic Aspects of Ergodic Theory can serve as a valuable foundation for doing research at the intersection of ergodic theory and operator theory

Author : I. P. Cornfeld,S. V. Fomin,Y. G. Sinai
Publisher : Springer Science & Business Media
Page : 487 pages
File Size : 52,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461569275

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Ergodic Theory by I. P. Cornfeld,S. V. Fomin,Y. G. Sinai Pdf

Ergodic theory is one of the few branches of mathematics which has changed radically during the last two decades. Before this period, with a small number of exceptions, ergodic theory dealt primarily with averaging problems and general qualitative questions, while now it is a powerful amalgam of methods used for the analysis of statistical properties of dyna mical systems. For this reason, the problems of ergodic theory now interest not only the mathematician, but also the research worker in physics, biology, chemistry, etc. The outline of this book became clear to us nearly ten years ago but, for various reasons, its writing demanded a long period of time. The main principle, which we adhered to from the beginning, was to develop the approaches and methods or ergodic theory in the study of numerous concrete examples. Because of this, Part I of the book contains the description of various classes of dynamical systems, and their elementary analysis on the basis of the fundamental notions of ergodicity, mixing, and spectra of dynamical systems. Here, as in many other cases, the adjective" elementary" i~ not synonymous with "simple. " Part II is devoted to "abstract ergodic theory. " It includes the construc tion of direct and skew products of dynamical systems, the Rohlin-Halmos lemma, and the theory of special representations of dynamical systems with continuous time. A considerable part deals with entropy.

Author : Karl E. Petersen,Karl Petersen
Publisher : Cambridge University Press
Page : 348 pages
File Size : 52,7 Mb
Release : 1989-11-23
Category : Mathematics
ISBN : 0521389976

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Ergodic Theory by Karl E. Petersen,Karl Petersen Pdf

The study of dynamical systems forms a vast and rapidly developing field even when one considers only activity whose methods derive mainly from measure theory and functional analysis. Karl Petersen has written a book which presents the fundamentals of the ergodic theory of point transformations and then several advanced topics which are currently undergoing intense research. By selecting one or more of these topics to focus on, the reader can quickly approach the specialized literature and indeed the frontier of the area of interest. Each of the four basic aspects of ergodic theory - examples, convergence theorems, recurrence properties, and entropy - receives first a basic and then a more advanced, particularized treatment. At the introductory level, the book provides clear and complete discussions of the standard examples, the mean and pointwise ergodic theorems, recurrence, ergodicity, weak mixing, strong mixing, and the fundamentals of entropy. Among the advanced topics are a thorough treatment of maximal functions and their usefulness in ergodic theory, analysis, and probability, an introduction to almost-periodic functions and topological dynamics, a proof of the Jewett-Krieger Theorem, an introduction to multiple recurrence and the Szemeredi-Furstenberg Theorem, and the Keane-Smorodinsky proof of Ornstein's Isomorphism Theorem for Bernoulli shifts. The author's easily-readable style combined with the profusion of exercises and references, summaries, historical remarks, and heuristic discussions make this book useful either as a text for graduate students or self-study, or as a reference work for the initiated.

Author : Ulrich Krengel,Karin Richter,Volker Warstat
Publisher : Unknown
Page : 248 pages
File Size : 53,7 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662173816

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Ergodic Theory and Related Topics III by Ulrich Krengel,Karin Richter,Volker Warstat Pdf

Author : Karma Dajani,Charlene Kalle
Publisher : CRC Press
Page : 268 pages
File Size : 45,6 Mb
Release : 2021-07-04
Category : Mathematics
ISBN : 9781000402773

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A First Course in Ergodic Theory by Karma Dajani,Charlene Kalle Pdf

A First Course in Ergodic Theory provides readers with an introductory course in Ergodic Theory. This textbook has been developed from the authors’ own notes on the subject, which they have been teaching since the 1990s. Over the years they have added topics, theorems, examples and explanations from various sources. The result is a book that is easy to teach from and easy to learn from — designed to require only minimal prerequisites. Features Suitable for readers with only a basic knowledge of measure theory, some topology and a very basic knowledge of functional analysis Perfect as the primary textbook for a course in Ergodic Theory Examples are described and are studied in detail when new properties are presented.

Author : David Kerr,Hanfeng Li
Publisher : Springer
Page : 431 pages
File Size : 42,5 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.