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Thermodynamic Formalism and Applications to Dimension Theory de Luis Barreira

Thermodynamic Formalism and Applications to Dimension Theory: Progress in Mathematics, cartea 294

Autor Luis Barreira
en Limba Engleză Hardback – 24 aug 2011
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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Specificații

ISBN-13: 9783034802055
ISBN-10: 3034802056
Pagini: 304
Ilustrații: XII, 300 p.
Dimensiuni: 155 x 235 x 25 mm
Greutate: 0.52 kg
Ediția:2011
Editura: Springer
Colecția Birkhäuser
Seria Progress in Mathematics

Locul publicării:Basel, Switzerland

Public țintă

Research

Cuprins

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.

Recenzii

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 and applying the thermodynamic formalism to prove results in the dimension theory of dynamical systems.” (Thomas Michael Jordan, Mathematical Reviews, March, 2014)

Textul de pe ultima copertă

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.

Caracteristici

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. Includes supplementary material: sn.pub/extras