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Ergodicity and Ergodic Points

  • Giovanni Gallavotti
  • Federico Bonetto
  • Guido Gentile
Chapter
Part of the Texts and Monographs in Physics book series (TMP)

Abstract

The problem of determining which sets are visited with defined frequency by the motions of a dynamical system (Ω, S) can be satisfactorily solved in the case of particularly simple systems; for instance in the case in which \(S = {S_{{t_0}}}\) and (S t )t∈ℝ is a Hamiltonian flow which is analytically integrable on a region W ⊂ ℝ2r and Ω = W, cf. definition 1.3.1. This means looking at motions observed at time intervals t 0. More precisely the following proposition holds.

Keywords

Rotation Number Ergodic Measure Ergodic Property Exceptional Point Irrational Rotation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliographical Note to Sect. 2.4

  1. [Ru66]
    Ruelle, D.: States of classical statistical mechanics, Communications in Mathematical Physics 3 (1966), 133–150.MathSciNetADSMATHCrossRefGoogle Scholar
  2. [Ru69]
    Ruelle, D.: Statistical mechanics, Benjamin, New York, 1969MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Giovanni Gallavotti
    • 1
  • Federico Bonetto
    • 2
  • Guido Gentile
    • 3
  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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