Special Problems in Chaotic Dynamics

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


A general theorem on Anosov maps allows us to say that in a certain sense Anosov maps that are close enough in C 2 can be considered as derived one from the other by a “change of coordinates”, which, however, is not really smooth. This is the theorem of structural stability of Anosov that can be formulated as follows.


Chaotic Dynamics Unstable Manifold Hard Core Symbolic Representation Gibbs State 
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Bibliographical Note

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    Shields, P.: The theory of Bernoulli shifts, University of Chicago Press, Chicago, 1973.zbMATHGoogle Scholar
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    Ornstein, D.: Ergodic theory, randomness and dynamical systems, Yale Mathematical Monographs, no. 5, Yale University Press, New Haven, 1974.zbMATHGoogle Scholar
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    Gallavotti, G.: Ising model and Bernouilli schemes in one dimesnion, Communications in Mathematical Physics 32 (1973), 183–190.MathSciNetADSzbMATHCrossRefGoogle Scholar
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    Ledrappier, F.: Mesure d’équilibre sur un reseau, Communications in Mathematical Physics 33 (1973), 119–128.MathSciNetADSzbMATHCrossRefGoogle Scholar
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    Monroy, G., Russo, L.: A family of codes between Markov and Bernoulli schemes, Communications in Mathematical Physics 43 (1975), 155–159.MathSciNetADSzbMATHCrossRefGoogle Scholar
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    Ornstein, D., Weiss, B.: unpublished (1974).Google Scholar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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