Thermodynamic Formalism and Applications to Dimension Theory

2011
ISBN: 978-3-0348-0336-6
Verlag: Springer

Buch, Englisch, 300 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 476 g

Reihe: Progress in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Barreira, Luis

Fachgebiete

• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Physik Thermodynamik

Inhaltsverzeichnis

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.