Preface

Summary

In recent years methods borrowed from thermodynamics and statistical mechanics have turned out to be very successful for the quantitative analysis and description of chaotic dynamical systems. These methods, originating from the pioneering work of Sinai, Ruelle, and Bowen in the early seventies on the thermodynamic formalism of dynamical systems, have been further developed in the mean time and have attracted strong interest among physicists. The quantitative characterization of chaotic motion by thermodynamic means and the thermodynamic analysis of multifractal sets are now an important and rapidly evolving branch of nonlinear science, with applications in many different areas.

The present book aims at an elucidation of the various thermodynamic concepts used for the analysis of nonlinear dynamical systems. It is intended to be an elementary introduction. We felt the need to write an easily readable book, because so far there exist only a few classical monographs on the subject that are written for mathematicians rather than physicists. Consequently, we have tried to write in the physicist's language. We have striven for a form that is readable for anybody with the knowledge of mathematics a student of physics or chemistry at the early graduate level would have. No advanced mathematical preknowledge on the part of the reader is required. On the other hand, we also tried to avoid serious loss of rigour in our presentation.