Dynamical Systems And Ergodic Theory

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Dynamical Systems And Ergodic Theory

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Author : Mark Pollicott
language : en
Publisher:
Release Date : 2013-07-13

Dynamical Systems And Ergodic Theory written by Mark Pollicott and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-13 with categories.

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

Ergodic Theory And Dynamical Systems

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Author : Yves Coudène
language : en
Publisher: Springer
Release Date : 2016-11-10

Ergodic Theory And Dynamical Systems written by Yves Coudène and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-10 with Mathematics categories.

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 Ergodic Theory And Applications

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Author : L.A. Bunimovich
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-04-05

Dynamical Systems Ergodic Theory And Applications written by L.A. Bunimovich and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-05 with Mathematics categories.

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.

Ergodic Theory

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Author : Manfred Einsiedler
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-11

Ergodic Theory written by Manfred Einsiedler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-11 with Mathematics categories.

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.

Random Dynamical Systems

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Author : Ludwig Arnold
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Random Dynamical Systems written by Ludwig Arnold and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.

Background and Scope of the Book This book continues, extends, and unites various developments in the intersection of probability theory and dynamical systems. I will briefly outline the background of the book, thus placing it in a systematic and historical context and tradition. Roughly speaking, a random dynamical system is a combination of a measure-preserving dynamical system in the sense of ergodic theory, (D,F,lP', (B(t))tE'lf), 'II'= JR+, IR, z+, Z, with a smooth (or topological) dy namical system, typically generated by a differential or difference equation :i: = f(x) or Xn+l = tp(x.,), to a random differential equation :i: = f(B(t)w,x) or random difference equation Xn+l = tp(B(n)w, Xn)· Both components have been very well investigated separately. However, a symbiosis of them leads to a new research program which has only partly been carried out. As we will see, it also leads to new problems which do not emerge if one only looks at ergodic theory and smooth or topological dynam ics separately. From a dynamical systems point of view this book just deals with those dynamical systems that have a measure-preserving dynamical system as a factor (or, the other way around, are extensions of such a factor). As there is an invariant measure on the factor, ergodic theory is always involved.

Dynamical Systems And Ergodic Theory

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Author : Mark Pollicott
language : en
Publisher: Cambridge University Press
Release Date : 1998-01-29

Dynamical Systems And Ergodic Theory written by Mark Pollicott and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-29 with Mathematics categories.

This book is an essentially self contained introduction to topological dynamics and ergodic theory. It is 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 particular audience. Parts of the book are suitable for a final year undergraduate course or for a masters level course. A number of applications are given, principally to number theory and arithmetic progressions (through van der waerden's theorem and szemerdi's theorem).

Ergodic Theory And Topological Dynamics Of Group Actions On Homogeneous Spaces

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Author : M. Bachir Bekka
language : en
Publisher: Cambridge University Press
Release Date : 2000-05-11

Ergodic Theory And Topological Dynamics Of Group Actions On Homogeneous Spaces written by M. Bachir Bekka and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-05-11 with Mathematics categories.

This book, first published in 2000, focuses on developments in the study of geodesic flows on homogenous spaces.

Ergodic Theory Of Random Transformations

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Author : Yuri Kifer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Ergodic Theory Of Random Transformations written by Yuri Kifer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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.

Ergodic Theory Hyperbolic Dynamics And Dimension Theory

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Author : Luís Barreira
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-04-28

Ergodic Theory Hyperbolic Dynamics And Dimension Theory written by Luís Barreira and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-28 with Mathematics categories.

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

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Author : I. P. Cornfeld
language : en
Publisher: Springer
Release Date : 2012-07-02

Ergodic Theory written by I. P. Cornfeld and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-02 with Mathematics categories.

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.