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 detaileddiscussion 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. First comprehensive exposition of several main extensions of the thermodynamic formalism. The emphasis of the text is on the relation to dimension theory and multifractal analysis. Includes a discussion of very recent results in the area as well as some open problems. The text is self-contained and all the results are included with detailed proofs. INDICE: 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. 8Limit Sets of Geometric Constructions. 9 Entropy Spectra. IV Almost Additive Thermodynamic Formalism. 10 Almost Additive Sequences. 11 Nonconformal Repellers. 12 Multifractal Analysis. Bibliography.
- ISBN: 978-3-0348-0205-5
- Editorial: Springer Basel
- Encuadernacion: Cartoné
- Páginas: 292
- Fecha Publicación: 30/09/2011
- Nº Volúmenes: 1
- Idioma: Inglés