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...

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Bibliographische Detailangaben
1. Verfasser: Barreira, Luís Manuel, 1968-
Format: Livre numérique
Sprache:Anglais
Veröffentlicht: Berlin, Heidelberg : Springer Berlin Heidelberg [20..].
Cham : Springer Nature
Ausgabe:1st ed. 2012.
Schriftenreihe:Universitext
Schlagworte:
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Edition sous un autre format:• Ergodic theory, hyperbolic dynamics and dimension theory, Luis Barreira, Berlin, Springer, 2012, 1 vol. (XII-290 p.), Universitext, 978-3-642-28089-4
• Ergodic Theory, Hyperbolic Dynamics and Dimension Theory, Texte imprimé, 9783642280917
• Ergodic theory, hyperbolic dynamics and dimension theory, Luis Barreira, Berlin, Springer, 2012, 1 vol. (XII-290 p.), Universitext, 978-3-642-28089-4
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505 1 |a 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 
505 0 |a Preface -- I Ergodic Theory -- II Entropy and Pressure -- III Hyperbolic Dynamics -- IV Dimension Theory -- Bibliography -- Index. -- 1.Basic Notions and Examples -- 2.Further Topics -- 3.Metric Entropy and Topological Entropy -- 4.Thermodynamic Formalism. -- 5.Basic Notions and Examples -- 6.Invariant Manifolds and Markov Partitions -- 7.Basic Notions and Examples -- 8.Dimension Theory of Hyperbolic Dynamics -- A Notions from Measure Theory 
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520 |a 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 
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