Overview
- Provides a concise introduction to ergodic theory and dynamical systems
- Presents numerous examples in detail
- Technically sound and up-to-date, with an approach that favors generality
Part of the book series: Universitext (UTX)
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About this book
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.
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.
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Keywords
Table of contents (18 chapters)
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Front Matter
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Ergodic Theory
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Front Matter
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Dynamical Systems
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Front Matter
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Entropy Theory
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Front Matter
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Ergodic Decomposition
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Front Matter
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Reviews
“This textbook is addressed to graduate students as well as to researchers who are not experts in ergodic theory and theory of dynamical systems. For an introduction to the subject it is a very good modern source.” (Ivan Podvigin, zbMATH, August, 2017)
“This 200-page book covers most relevant topics for a course in ergodic theory and dynamical systems, addressing topological and measure theoretic perspectives, and including notions of entropy. The subjects are illustrated with selected examples and bibliographical notes on the development of the theory. It is a delightful brief introduction, designed to be a course book on the theme.” (Túlio O. Carvalho, Mathematical Reviews, August, 2017)
Authors and Affiliations
About the author
Yves Coudène is a full professor at Brest University, France. His research areas include hyperbolic dynamics, ergodic theory and the geometry of negatively curved spaces.
Bibliographic Information
Book Title: Ergodic Theory and Dynamical Systems
Authors: Yves Coudène
Translated by: Reinie Erné
Series Title: Universitext
DOI: https://doi.org/10.1007/978-1-4471-7287-1
Publisher: Springer London
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag London 2016
Softcover ISBN: 978-1-4471-7285-7Published: 21 November 2016
eBook ISBN: 978-1-4471-7287-1Published: 10 November 2016
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XIII, 190
Number of Illustrations: 48 b/w illustrations, 1 illustrations in colour
Additional Information: Jointly published with EDP Sciences, Les Ulis, France. Original French edition published by EDP Sciences, Les Ulis, France and CNRS Editions, Paris, France