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© 2004

Aspects of Ergodic, Qualitative and Statistical Theory of Motion

Book

Part of the Texts and Monographs in Physics book series (TMP)

Table of contents

  1. Front Matter
    Pages I-X
  2. Giovanni Gallavotti, Federico Bonetto, Guido Gentile
    Pages 1-26
  3. Giovanni Gallavotti, Federico Bonetto, Guido Gentile
    Pages 27-71
  4. Giovanni Gallavotti, Federico Bonetto, Guido Gentile
    Pages 73-108
  5. Giovanni Gallavotti, Federico Bonetto, Guido Gentile
    Pages 109-153
  6. Giovanni Gallavotti, Federico Bonetto, Guido Gentile
    Pages 155-187
  7. Giovanni Gallavotti, Federico Bonetto, Guido Gentile
    Pages 189-226
  8. Giovanni Gallavotti, Federico Bonetto, Guido Gentile
    Pages 227-289
  9. Giovanni Gallavotti, Federico Bonetto, Guido Gentile
    Pages 291-325
  10. Giovanni Gallavotti, Federico Bonetto, Guido Gentile
    Pages 327-357
  11. Giovanni Gallavotti, Federico Bonetto, Guido Gentile
    Pages 359-396
  12. Back Matter
    Pages 397-438

About this book

Introduction

 Intended for beginners in ergodic theory, this book 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 theory. Many examples illustrate the ideas and, in addition, a substantial number of interesting topics are treated in the form of guided problems.

Keywords

Asonov Theory Chaotic Dynamics Ergodic Theory of Maps Ergodicity Gibbs State KAM Theory Renormalization group mathematical physics

Authors and affiliations

  1. 1.Dipartimento di FisicaUniversità degli Studi di Roma “La Sapienza”RomaItaly
  2. 2.School of Mathematics Georgia TechAtlantaUSA
  3. 3.Dipartimento di MatematicaUniversità Roma TreRomaItaly

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Reviews

From the reviews:

"The book is centered on the symbiotic relationship between ergodic theory and statistical mechanics, in particular on its modern applications to chaotic and non-chaotic dynamical systems. In slightly more than 400 pages the authors … discuss in detail important applications of the theory. This is achieved by treating many important and interesting questions as ‘guided problems’ … . the entire book is tightly and nicely knitted together." (Luc Rey-Bellet, Mathematical Reviews, 2005h)

"The main novelty is the systematic treatment of a few characteristic problems of ergodic theory by a unified method in terms of convergent or divergent power series expansions. … The problems at the end of every section are an essential complement to the text … ." (Nasir N. Ganikhodjaev, Zentralblatt MATH, Vol. 1065, 2005)