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Mathematics - Dynamical Systems & Differential Equations | Ergodic Theory, Hyperbolic Dynamics and Dimension Theory

Ergodic Theory, Hyperbolic Dynamics and Dimension Theory

Series: Universitext

Barreira, Luis

2012, XII, 290 p. 34 illus.

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  • ​​​​​​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

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.

Content Level » Graduate

Keywords » 37AXX, 37DXX, 37C45 - dimension theory - entropy theory - ergodic theory - hyperbolic dynamics - thermodynamic formalism

Related subjects » Dynamical Systems & Differential Equations

Table of contents 

Preface.- I Ergodic Theory.- 1.Basic Notions and Examples.- 2.Further Topics.- II Entropy and Pressure.- 3.Metric Entropy and Topological Entropy.- 4.Thermodynamic Formalism. III Hyperbolic Dynamics.- 5.Basic Notions and Examples.- 6.Invariant Manifolds and Markov Partitions.- IV Dimension Theory.- 7.Basic Notions and Examples.- 8.Dimension Theory of Hyperbolic Dynamics.- A Notions from Measure Theory.- Bibliography.- Index. ​

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