Thermodynamic Formalism and Applications to Dimension Theory

This volume provides a unified exposition of thermodynamic formalism and some of its main extensions, with an emphasis on the relation to the dimension theory and the multifractal analysis of dynamical systems. It also includes a discussion of the most substantial applications.

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.