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Birkhäuser - Birkhäuser Mathematics | Thermodynamic Formalism and Applications to Dimension Theory

Thermodynamic Formalism and Applications to Dimension Theory

Series: Progress in Mathematics, Vol. 294

Barreira, Luis

2011, XII, 300 p.

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  • 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.

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.

Content Level » Research

Keywords » dimension theory - multifractal analysis - thermodynamic formalism

Related subjects » Birkhäuser Mathematics

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