Ergodic Theory And Dynamical Systems

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Ergodic Theory and Dynamical Systems

Yves Coudène
Ergodic Theory and Dynamical Systems Book PDF

Author : Yves Coudène
Publisher : Springer
Page : 190 pages
File Size : 46,9 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.

Dynamical Systems and Ergodic Theory

Mark Pollicott,Michiko Yuri
Dynamical Systems and Ergodic Theory Book PDF

Author : Mark Pollicott,Michiko Yuri
Publisher : Unknown
Page : 128 pages
File Size : 40,8 Mb
Release : 2013-07-13
Category : Electronic
ISBN : 1299733905

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Dynamical Systems and Ergodic Theory by Mark Pollicott,Michiko Yuri Pdf

Essentially a self-contained text giving an introduction to topological dynamics and ergodic theory.

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 : 55,5 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.

Dynamical Systems, Ergodic Theory and Applications

L.A. Bunimovich,S.G. Dani,R.L. Dobrushin,M.V. Jakobson,I.P. Kornfeld,N.B. Maslova,Ya.B. Pesin,J. Smillie,Yu.M. Sukhov,A.M. Vershik
Dynamical Systems Ergodic Theory and Applications Book PDF

Author : L.A. Bunimovich,S.G. Dani,R.L. Dobrushin,M.V. Jakobson,I.P. Kornfeld,N.B. Maslova,Ya.B. Pesin,J. Smillie,Yu.M. Sukhov,A.M. Vershik
Publisher : Springer Science & Business Media
Page : 476 pages
File Size : 46,8 Mb
Release : 2000-04-05
Category : Mathematics
ISBN : 3540663169

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Dynamical Systems, Ergodic Theory and Applications by L.A. Bunimovich,S.G. Dani,R.L. Dobrushin,M.V. Jakobson,I.P. Kornfeld,N.B. Maslova,Ya.B. Pesin,J. Smillie,Yu.M. Sukhov,A.M. Vershik Pdf

This EMS volume, the first edition of which was published as Dynamical Systems II, EMS 2, familiarizes the reader with the fundamental ideas and results of modern ergodic theory and its applications to dynamical systems and statistical mechanics. The enlarged and revised second edition adds two new contributions on ergodic theory of flows on homogeneous manifolds and on methods of algebraic geometry in the theory of interval exchange transformations.

Smooth Ergodic Theory of Random Dynamical Systems

Pei-Dong Liu,Min Qian
Smooth Ergodic Theory of Random Dynamical Systems Book PDF

Author : Pei-Dong Liu,Min Qian
Publisher : Springer
Page : 233 pages
File Size : 55,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540492917

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Smooth Ergodic Theory of Random Dynamical Systems by Pei-Dong Liu,Min Qian Pdf

This book studies ergodic-theoretic aspects of random dynam- ical systems, i.e. of deterministic systems with noise. It aims to present a systematic treatment of a series of recent results concerning invariant measures, entropy and Lyapunov exponents of such systems, and can be viewed as an update of Kifer's book. An entropy formula of Pesin's type occupies the central part. The introduction of relation numbers (ch.2) is original and most methods involved in the book are canonical in dynamical systems or measure theory. The book is intended for people interested in noise-perturbed dynam- ical systems, and can pave the way to further study of the subject. Reasonable knowledge of differential geometry, measure theory, ergodic theory, dynamical systems and preferably random processes is assumed.

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 : 42,7 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.

Ergodic Theory

Idris Assani
Ergodic Theory Book PDF

Author : Idris Assani
Publisher : Walter de Gruyter GmbH & Co KG
Page : 148 pages
File Size : 54,5 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

I. P. Cornfeld,S. V. Fomin,Y. G. Sinai
Ergodic Theory Book PDF

Author : I. P. Cornfeld,S. V. Fomin,Y. G. Sinai
Publisher : Springer Science & Business Media
Page : 487 pages
File Size : 51,9 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.

Ergodic Theory, Open Dynamics, and Coherent Structures

Wael Bahsoun,Christopher Bose,Gary Froyland
Ergodic Theory Open Dynamics and Coherent Structures Book PDF

Author : Wael Bahsoun,Christopher Bose,Gary Froyland
Publisher : Springer Science & Business
Page : 227 pages
File Size : 45,6 Mb
Release : 2014-05-02
Category : Mathematics
ISBN : 9781493904198

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Ergodic Theory, Open Dynamics, and Coherent Structures by Wael Bahsoun,Christopher Bose,Gary Froyland Pdf

This book is comprised of selected research articles developed from a workshop on Ergodic Theory, Probabilistic Methods and Applications, held in April 2012 at the Banff International Research Station. It contains contributions from world leading experts in ergodic theory, numerical dynamical systems, molecular dynamics and ocean/atmosphere dynamics, nonequilibrium statistical mechanics. The volume will serve as a valuable reference for mathematicians, physicists, engineers, biologists and climate scientists, who currently use, or wish to learn how to use, probabilistic techniques to cope with dynamical models that display open or non-equilibrium behavior.

Random Dynamical Systems

Ludwig Arnold
Random Dynamical Systems Book PDF

Author : Ludwig Arnold
Publisher : Springer Science & Business Media
Page : 590 pages
File Size : 47,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662128787

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Random Dynamical Systems by Ludwig Arnold Pdf

The first systematic presentation of the theory of dynamical systems under the influence of randomness, this book includes products of random mappings as well as random and stochastic differential equations. The basic multiplicative ergodic theorem is presented, providing a random substitute for linear algebra. On its basis, many applications are detailed. Numerous instructive examples are treated analytically or numerically.

Ergodic Theory and Harmonic Analysis

Karl E. Petersen
Ergodic Theory and Harmonic Analysis Book PDF

Author : Karl E. Petersen
Publisher : Cambridge University Press
Page : 452 pages
File Size : 50,6 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.

Introduction to the Modern Theory of Dynamical Systems

Anatole Katok,A. B. Katok,Boris Hasselblatt
Introduction to the Modern Theory of Dynamical Systems Book PDF

Author : Anatole Katok,A. B. Katok,Boris Hasselblatt
Publisher : Cambridge University Press
Page : 828 pages
File Size : 50,6 Mb
Release : 1995
Category : Mathematics
ISBN : 0521575575

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Introduction to the Modern Theory of Dynamical Systems by Anatole Katok,A. B. Katok,Boris Hasselblatt Pdf

A self-contained comprehensive introduction to the mathematical theory of dynamical systems for students and researchers in mathematics, science and engineering.

Recurrence in Ergodic Theory and Combinatorial Number Theory

Harry Furstenberg
Recurrence in Ergodic Theory and Combinatorial Number Theory Book PDF

Author : Harry Furstenberg
Publisher : Princeton University Press
Page : 216 pages
File Size : 53,6 Mb
Release : 2014-07-14
Category : Mathematics
ISBN : 9781400855162

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Recurrence in Ergodic Theory and Combinatorial Number Theory by Harry Furstenberg Pdf

Topological dynamics and ergodic theory usually have been treated independently. H. Furstenberg, instead, develops the common ground between them by applying the modern theory of dynamical systems to combinatories and number theory. Originally published in 1981. 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 : 44,9 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 of Random Transformations

Yuri Kifer
Ergodic Theory of Random Transformations Book PDF

Author : Yuri Kifer
Publisher : Springer Science & Business Media
Page : 221 pages
File Size : 49,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468491753

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Ergodic Theory of Random Transformations by Yuri Kifer Pdf

Ergodic theory of dynamical systems i.e., the qualitative analysis of iterations of a single transformation is nowadays a well developed theory. In 1945 S. Ulam and J. von Neumann in their short note [44] suggested to study ergodic theorems for the more general situation when one applies in turn different transforma tions chosen at random. Their program was fulfilled by S. Kakutani [23] in 1951. 'Both papers considered the case of transformations with a common invariant measure. Recently Ohno [38] noticed that this condition was excessive. Ergodic theorems are just the beginning of ergodic theory. Among further major developments are the notions of entropy and characteristic exponents. The purpose of this book is the study of the variety of ergodic theoretical properties of evolution processes generated by independent applications of transformations chosen at random from a certain class according to some probability distribution. The book exhibits the first systematic treatment of ergodic theory of random transformations i.e., an analysis of composed actions of independent random maps. This set up allows a unified approach to many problems of dynamical systems, products of random matrices and stochastic flows generated by stochastic differential equations.