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Thermodynamic Formalism and Applications to Dimension Theory [electronic resource] / by Luis Barreira.

By: Barreira, Luis [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Progress in Mathematics: 294Publisher: Basel : Springer Basel, 2011Description: XII, 300 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783034802062.Subject(s): Mathematics | Differentiable dynamical systems | Mathematics | Dynamical Systems and Ergodic TheoryDDC classification: 515.39 | 515.48 Online resources: Click here to access online
Contents:
Preface -- 1 Introduction -- I Classical Thermodynamic Formalism -- 2 Thermodynamic Formalism: Basic Notions -- 3 The Case of Symbolic Dynamics -- II Nonadditive Thermodynamic Formalism -- 4 Nonadditive Thermodynamic Formalism -- 5 Dimension Estimates for Repellers -- 6 Dimension Estimates for Hyperbolic Sets -- III Subadditive Thermodynamic Formalism -- 7 Asymptotically Subadditive Sequences -- 8 Limit Sets of Geometric Constructions -- 9 Entropy Spectra -- IV Almost Additive Thermodynamic Formalism -- 10 Almost Additive Sequences -- 11 Nonconformal Repellers -- 12 Multifractal Analysis -- Bibliography.
In: Springer eBooksSummary: This self-contained monograph presents a unified exposition of the thermodynamic formalism and some of its main extensions, with emphasis on the relation to dimension theory and multifractal analysis of dynamical systems. In particular, the book considers three different flavors of the thermodynamic formalism, namely nonadditive, subadditive, and almost additive, and provides a detailed discussion of some of the most significant results in the area, some of them quite recent. It also includes a discussion of the most substantial applications of these flavors of the thermodynamic formalism to dimension theory and multifractal analysis of dynamical systems.
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Preface -- 1 Introduction -- I Classical Thermodynamic Formalism -- 2 Thermodynamic Formalism: Basic Notions -- 3 The Case of Symbolic Dynamics -- II Nonadditive Thermodynamic Formalism -- 4 Nonadditive Thermodynamic Formalism -- 5 Dimension Estimates for Repellers -- 6 Dimension Estimates for Hyperbolic Sets -- III Subadditive Thermodynamic Formalism -- 7 Asymptotically Subadditive Sequences -- 8 Limit Sets of Geometric Constructions -- 9 Entropy Spectra -- IV Almost Additive Thermodynamic Formalism -- 10 Almost Additive Sequences -- 11 Nonconformal Repellers -- 12 Multifractal Analysis -- Bibliography.

This self-contained monograph presents a unified exposition of the thermodynamic formalism and some of its main extensions, with emphasis on the relation to dimension theory and multifractal analysis of dynamical systems. In particular, the book considers three different flavors of the thermodynamic formalism, namely nonadditive, subadditive, and almost additive, and provides a detailed discussion of some of the most significant results in the area, some of them quite recent. It also includes a discussion of the most substantial applications of these flavors of the thermodynamic formalism to dimension theory and multifractal analysis of dynamical systems.

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