Advertisement

Ordering Chaos

  • Giovanni Gallavotti
Chapter
  • 431 Downloads
Part of the Texts and Monographs in Physics book series (TMP)

Abstract

After the discussions of the previous chapters it becomes imperative to find quantitative methods of study, or even simply of description, of the various phenomena that one expects to observe in experiments on fluids.

Keywords

Lyapunov Exponent Continuous Spectrum Periodic Point Unstable Manifold Stable Manifold 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. [AA68]
    Arnold, V.I., Avez, A.: Ergodic problems of classical mechanics, Ben-jamin, New York, 1968.Google Scholar
  2. Ga81] Gallavotti, G.: Aspetti della teoria ergodica qualitativa e statistica del moto, “Quaderni dell’ Unione Matematica Italiana”, vol. 21, Pitagora editrice, Bologna, 1981. Copies can be obtained by writing to “U.M.I., Dip. Matematica, Università di Bologna, P.zza di Porta S. Donato, 5, 40127, Bologna”, or to “Editrice Pitagora, Via Zamboni 57, 40127 Bologna” (Lit. 8000).Google Scholar
  3. Ga95a] Gallavotti, G.: Reversible Anosov maps and large deviations,Mathematical Physics Electronic Journal, MPEJ, (http:// mpej.unige.ch), 1 1–12, 1995.Google Scholar
  4. [ER81]
    Eckmann, J.P., Ruelle, D.: Ergodic theory of chaos and strange attrac-tors, Reviews of Modern Physics, 57, 617–656, 1981.MathSciNetADSCrossRefGoogle Scholar
  5. [Ga82]
    Gallavotti, G.: The Dirichlet problem and the Perron-Frobenius theorem, Bollettino Unione Matematica Italiana, (6), 1B, 1029–1038, 1982.MathSciNetzbMATHGoogle Scholar
  6. [LY73]
    Lasota, A., Yorke, J.A.: On the existence of invariant measures for piece-wise monotonic transformations, Transactions American Mathematical Society, 183, 481, 1973.MathSciNetCrossRefGoogle Scholar
  7. [Sm67]
    Smale, S.: Differentiable dynamical systems, Bulletin of the American Mathematical Society, 73, 747–818, 1967.MathSciNetzbMATHCrossRefGoogle Scholar
  8. [AF91]
    Adler, R., Flatto, L.: Geodesic flows, interval maps and symbolic dy-namics, Bulletin of the American Mathematical Society, 25, 229–334, 1991.zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Giovanni Gallavotti
    • 1
  1. 1.Dipartmento di Fisica, I.N.F.N.Università degli Studi di Roma “La Sapienza”RomaItaly

Personalised recommendations