Overview
- 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
Part of the book series: Progress in Mathematics (PM, volume 294)
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Table of contents (12 chapters)
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Front Matter
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Classical Thermodynamic Formalism
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Front Matter
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Nonadditive Thermodynamic Formalism
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Front Matter
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Subadditive Thermodynamic Formalism
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Front Matter
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Almost Additive Thermodynamic Formalism
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
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)Authors and Affiliations
Bibliographic Information
Book Title: Thermodynamic Formalism and Applications to Dimension Theory
Authors: Luis Barreira
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/978-3-0348-0206-2
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Basel AG 2011
Hardcover ISBN: 978-3-0348-0205-5Published: 24 August 2011
Softcover ISBN: 978-3-0348-0336-6Published: 27 November 2013
eBook ISBN: 978-3-0348-0206-2Published: 24 August 2011
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 1
Number of Pages: XII, 300