Ergodicity and Ergodic Points

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


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.


Rotation Number Ergodic Measure Ergodic Property Exceptional Point Irrational Rotation 
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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.MathSciNetADSzbMATHCrossRefGoogle Scholar
  2. [Ru69]
    Ruelle, D.: Statistical mechanics, Benjamin, New York, 1969zbMATHGoogle 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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