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SMF/AMS Texts and Monographs - Titles - 2 (2000)

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Thermodynamic Formalism and Holomorphic Dynamical Systems
Publié en français dans le numéro 4 (1996) de la série Panoramas et Synthèses
Michel Zinsmeister (translated by C. Greg Anderson)
Société Mathématique de France et AmericanMathematical Society
SMF/AMS Texts and Monographs 2 (2000), 91 pages
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Abstract:
The purpose of thermodynamics and statistical physics isto understand theequilibrium of a gas or the different states of matter. To understand thestrange fractalsets appearing when one iterates a quadratic polynomial is one of the goalsof the theory ofholomorphic dynamical systems. These two theories are strongly linked: Thelaws ofthermodynamics happen to be an extremely powerful tool for understandingthe objects ofholomorphic dynamical systems. A ``thermodynamic formalism'' has beendeveloped, bringingtogether notions that are a priori unrelated. While the deep reasons ofthis parallelismremain unknown, the goal of this book is to describe this formalism bothfrom the physicaland mathematical point of view in order to understand how it works and howuseful it can be.This translation is a slightly revised version of the original Frenchedition. The mainchanges are in Chapters 5 and 6 and consist of clarification of some proofsand a newpresentation of the basics in iteration of polynomials.

Keywords: Ergodic Theory, Measure theory, Differentiable dynamical systems,Thermodynamics

Class. math. : 28Dxx, 30-XX, 80-XX, 82Bxx


ISSN : 1525-2302