Thermodynamic Formalism and Applications to Dimension Theory [Paperback]

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.

This volume provides a unified exposition of thermodynamic formalism and some of its main extensions, with an emphasis on the relation to the dimension theory and the multifractal analysis of dynamical systems. It also includes a discussion of the most substantial applications.

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.

From the reviews:

This book gives a detailed account of the connection between two areas of dynamical systems, the thermodynamic formalism and dimension theory in dynamical systems. & The book is probably best read by someone already familiar with the basics of ergodic theory, dynamical systems, and the Hausdorff dimension & . the book gives the reader a good grounding in both thermodynamical formalism anl37