Ergodic theory, hyperbolic dynamics and dimension theory
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...
| Main Author: | Barreira, Luís, 1968- |
|---|---|
| Other Authors: | SpringerLink (Online service) |
| Format: | eBook |
| Language: | English |
| Published: |
Berlin ; New York :
Springer,
©2012.
Berlin ; New York : [2012] |
| Physical Description: |
1 online resource (xii, 290 pages). |
| Series: |
Universitext.
|
| Subjects: |
| Summary: |
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. |
|---|---|
| Item Description: |
Includes bibliographical references and index. Part 1. Ergodic Theory -- Basic Notions and Examples -- Further Topics -- Introduction -- Part 2. Entropy and Pressure -- Metric Entropy and Topological Entropy -- Thermodynamic Formalism -- Part 3. Hyperbolic Dynamics -- Basic Notions and Examples -- Invariant Manifolds and Markov Partitions -- Part 4. Dimension Theory -- Basic Notions and Examples -- Dimension Theory of Hyperbolic Dynamics. 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. English. |
| Physical Description: |
1 online resource (xii, 290 pages). |
| Bibliography: |
Includes bibliographical references and index. |
| ISBN: |
9783642280900 3642280900 3642280897 9783642280894 |
| ISSN: |
0172-5939. |