Formalisme thermodynamique et systèmes dynamiques holomorphes / Michel Zinsmeister

Auteur: Zinsmeister, Michel (1956-) - AuteurType de document: MonographieCollection: Panoramas et synthèses ; 4Langue: françaisPays: FranceÉditeur: Paris : Société Mathématique de France, 1996Description: 1 vol. (vi-96 p.) : ill. ; 24 cm ISBN: 2856290515 ; br. Résumé: The purpose of this book is to present some pure mathematical results which are obtained as corollaries of physical laws, stating thus the symmetry between mathematics and physics. For that, the author chooses the example of two disciplines apparently unlinked: thermodynamics (a part of statistical physics which studies the equilibrium of a gas or of different states of matter) and holomorphical dynamical systems (a theory which analyzes, among other things, the strange fractal sets which appear when iterating a quadratic polynomial). The first part of the work is dedicated to the physical aspect of the problem: the so-called “thermodynamical formalism” is introduced (that is, the ergodic theory, the different notions of entropy, as well as a thermodynamical model). Next, the main tool of this book, the Perron-Frobenius-Ruelle theorem and its thermodynamical consequences are developed. (Zentralblatt).Bibliographie: Bibliogr. p. [95]-96. Sujets MSC: 37Axx Dynamical systems and ergodic theory -- Ergodic theory
37-02 Dynamical systems and ergodic theory -- Research exposition (monographs, survey articles)
37Fxx Dynamical systems and ergodic theory -- Complex dynamical systems
82B30 Statistical mechanics, structure of matter -- Equilibrium statistical mechanics -- Statistical thermodynamics
37Bxx Dynamical systems and ergodic theory -- Topological dynamics
En-ligne: Sommaire
Location Call Number Status Date Due
Couloir 11860-01 / Séries Panor 4 (Browse Shelf) Available

Bibliogr. p. [95]-96

The purpose of this book is to present some pure mathematical results which are obtained as corollaries of physical laws, stating thus the symmetry between mathematics and physics. For that, the author chooses the example of two disciplines apparently unlinked: thermodynamics (a part of statistical physics which studies the equilibrium of a gas or of different states of matter) and holomorphical dynamical systems (a theory which analyzes, among other things, the strange fractal sets which appear when iterating a quadratic polynomial). The first part of the work is dedicated to the physical aspect of the problem: the so-called “thermodynamical formalism” is introduced (that is, the ergodic theory, the different notions of entropy, as well as a thermodynamical model). Next, the main tool of this book, the Perron-Frobenius-Ruelle theorem and its thermodynamical consequences are developed. (Zentralblatt)

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