Intended for beginners in ergodic theory, this introductory textbook addresses students as well as researchers in mathematical physics. The main novelty is the systematic treatment of characteristic problems in ergodic theory by a unified method in terms of convergent power series and renormalization group methods, in particular. Basic concepts of ergodicity, like Gibbs states, are developed and applied to, e.g., Asonov systems or KAM Theroy. Many examples illustrate the ideas and, in addition, a substantial number of interesting topics are treated in the form of guided problems.

The Italian 1980 version of Gallavotti's book on ergodic theory of maps is a classic and the scientific community will certainly welcome its rebirth in this completely rewritten and greatly enlarged English edition Includes supplementary material: sn.pub/extras

Autorentext

Giovanni Gallavotti, emeritus, has been fellow at IHES (Paris, 1966-1968) with David Ruelle and post doc at Rockefeller University (New York, 1968-1970) with Mark Kac. He has been, since 1972, full professor in various universities (Napoli, Roma2 and Roma1). He has been long term visitor at IHES, IAS, Nijmegen, Princeton and Rutgers University. His primary research focused subsequently on theoretical and historical aspects of Equilibrium Statistical Mechanics, Quantum field theory, Low temperature Fermi systems, Nonequilibrium and, currently, concentrates on mathematical problems on Fluid mechanics. Recipient of several awards and prizes (Presidente della Repubblica prize, Boltzmann medal, Henri Poincare' prize).

Inhalt
1 General Qualitative Properties.- 2 Ergodicity and Ergodic Points.- 3 Entropy and Complexity.- 4 Markovian Pavements.- 5 Gibbs Distributions.- 6 General Properties of Gibbs and SRB Distributions.- 7 Analyticity, Singularity and Phase Transitions.- 8 Special Ergodic Theory Problems in Nonchaotic Dynamics.- 9 Some Special Topics in KAM Theory.- 10 Special Problems in Chaotic Dynamics.- A Nonequilibrium Thermodynamics? Twenty-Seven Comments.- Name Index.- Citations Index.