Overview
- Self-contained introduction to three main areas of current research
- Primarily intended for graduate students as well as researchers and useful as a self-study guide
- Gives a unified perspective of material that was dispersed so far in different sources
Part of the book series: Universitext (UTX)
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Table of contents (9 chapters)
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Front Matter
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Ergodic Theory
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Front Matter
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Entropy and Pressure
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Front Matter
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Hyperbolic Dynamics
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Front Matter
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Dimension Theory
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
From the reviews:
“This book gives an introduction to the fundamental ideas and results in the study of dynamical systems that lie at the interface of ergodic theory, thermodynamic formalism, hyperbolic dynamics, and dimension theory. It is targeted at readers, particularly graduate students, who are familiar with the general theory of measure and integration … . theory is developed in a self-contained manner and the book contains a wealth of exercises that give examples illustrating the concepts from the main text and also suggest further directions of exploration.” (Vaughn Climenhaga, Mathematical Reviews, July, 2013)
“This textbook is a careful and well thought out introduction to the dimension theory of dynamical systems, including a full development of the needed tools and examples from ergodic theory and hyperbolic dynamics. … the book is aimed at graduate students and researchers interested in learning about ergodic theory, dimension theory, or hyperbolic dynamics. A substantial number of exercises of varying levels is included, and the care with which the material is presented as a self-contained coherent account makes it viable for independent study.” (Thomas B. Ward, Zentralblatt MATH, Vol. 1262, 2013)Authors and Affiliations
About the author
Bibliographic Information
Book Title: Ergodic Theory, Hyperbolic Dynamics and Dimension Theory
Authors: Luis Barreira
Series Title: Universitext
DOI: https://doi.org/10.1007/978-3-642-28090-0
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2012
Softcover ISBN: 978-3-642-28089-4Published: 29 April 2012
eBook ISBN: 978-3-642-28090-0Published: 28 April 2012
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XII, 290
Number of Illustrations: 34 b/w illustrations