Formalisme thermodynamique et systèmes dynamiques holomorphes / Michel Zinsmeister

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)