Thermodynamic Formalism and Holomorphic Dynamical Systems

ISBN-13: 9780821819487 / Angielski / Miękka / 1999

Michel Zinsmeister

Opis

The purpose of thermodynamics and statistical physics is to understand the equilibrium of a gas or the different states of matter. To understand the strange fractal sets appearing when one iterates a quadratic polynomial is one of the goals of the theory of holomorphic dynamical systems. These two theories are strongly linked: the laws of thermodynamics happen to be an extremely powerful tool for understanding the objects of holomorphic dynamical systems. A thermodynamic formalism has been developed, bringing together notions that are a priori unrelated. While the deep reasons of this parallelism remain unknown, the goal of this book is to describe this formalism both from the physical and mathematical point of view in order to understand how it works and how useful it can be.