Thermodynamic formalism and holomorphic dynamical systems
著者
書誌事項
Thermodynamic formalism and holomorphic dynamical systems
（SMF/AMS texts and monographs, v. 2）（Panoramas et synthèses, no 4,
American Mathematical Society, c2000
- タイトル別名
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Formalisme thermodynamique et systèmes dynamiques holomorphes
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注記
Translation of: Formalisme thermodynamique et systèmes dynamiques holomorphes
Includes bibliographical references (p. 81-82)
内容説明・目次
内容説明
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. This translation is a slightly revised version of the original French edition. The main changes are in Chapters 5 and 6 and consist of clarification of some proofs and a new presentation of the basics in iteration of polynomials.
目次
Introduction The ergodic hypothesis The concept of entropy Entropy in ergodic theory The Perron-Frobenius-Ruelle theorem Conformal repellers Iteration of quadratic polynomials Phase transitions Hausdorff measures and dimension Bibliography.
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