Thermodynamic Formalism and Applications to Dimension Theory

• Main Author: Barreira, Luis (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Springer Basel, 2011.
• Series: Progress in Mathematics ; 294
• Subjects: Mathematics.; Dynamics.; Ergodic theory.; Dynamical Systems and Ergodic Theory.

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...

Table of 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.