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  • Book
  • © 2004

Aspects of Ergodic, Qualitative and Statistical Theory of Motion

  • 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

Part of the book series: Theoretical and Mathematical Physics (TMP)

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-X
  2. General Qualitative Properties

    • Giovanni Gallavotti, Federico Bonetto, Guido Gentile
    Pages 1-26
  3. Ergodicity and Ergodic Points

    • Giovanni Gallavotti, Federico Bonetto, Guido Gentile
    Pages 27-71
  4. Entropy and Complexity

    • Giovanni Gallavotti, Federico Bonetto, Guido Gentile
    Pages 73-108
  5. Markovian Pavements

    • Giovanni Gallavotti, Federico Bonetto, Guido Gentile
    Pages 109-153
  6. Gibbs Distributions

    • Giovanni Gallavotti, Federico Bonetto, Guido Gentile
    Pages 155-187
  7. General Properties of Gibbs and SRB Distributions

    • Giovanni Gallavotti, Federico Bonetto, Guido Gentile
    Pages 189-226
  8. Analyticity, Singularity and Phase Transitions

    • Giovanni Gallavotti, Federico Bonetto, Guido Gentile
    Pages 227-289
  9. Special Ergodic Theory Problems in Nonchaotic Dynamics

    • Giovanni Gallavotti, Federico Bonetto, Guido Gentile
    Pages 291-325
  10. Some Special Topics in KAM Theory

    • Giovanni Gallavotti, Federico Bonetto, Guido Gentile
    Pages 327-357
  11. Special Problems in Chaotic Dynamics

    • Giovanni Gallavotti, Federico Bonetto, Guido Gentile
    Pages 359-396
  12. Back Matter

    Pages 397-438

About this book

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.

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)

Authors and Affiliations

  • Dipartimento di Fisica, Università degli Studi di Roma “La Sapienza”, Roma, Italy

    Giovanni Gallavotti

  • School of Mathematics Georgia Tech, Atlanta, USA

    Federico Bonetto

  • Dipartimento di Matematica, Università Roma Tre, Roma, Italy

    Guido Gentile

Bibliographic Information

Buy it now

Buying options

eBook USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access