Turbulence : Determinism and chaos

  • Y. Pomeau
IX. Turbulence
Part of the Lecture Notes in Physics book series (LNP, volume 71)


Rayleigh Number Lorenz System Stable Fixed Point Lorenz Attractor Arrival Point 
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  1. 1.
    D. Ruelle, F. Takens, Comm. Math. Phys. 20, 167 (1971)CrossRefGoogle Scholar
  2. 2.
    P.R. Halmos,Ergodic theory, Chelsea Pub.Comp. New York (1956)Google Scholar
  3. 3.
    R. May, Nature 261, 459 (1976)CrossRefPubMedGoogle Scholar
  4. 4.
    T.Y. Li and J.A. Yorke, Am. Math. Month. 82, 985 (1975)Google Scholar
  5. 5.
    T. Rikitake, “Electromagnetism and the earth interior” Elsevier (1968)Google Scholar
  6. 6.
    C. Laj, Y. Pomeau, in preparationGoogle Scholar
  7. 7.
    Monin, Yaglom, “Statistical Fluid Mechanics”, Vol. 1–2, MIT Press (1971)Google Scholar
  8. 8.
    I. Kubo, notes from the Nagoya Univ.Google Scholar
  9. 8a.
    E. Hopf, “Ergodentheorie”, Spinger Verlag, Berlin (1937)Google Scholar
  10. 8b.
    M. Smorodinsky, “Ergodic Theory, Entropy”, Springer Verlag Lectures Notesin math. 2 14, Berlin (1971)Google Scholar
  11. 9.
    S. Smale, Bull. AMS 73, 747 (1967)Google Scholar
  12. 10.
    P.C. Martin and J.B. Mc Laughlin, Phys. Rev. Lett. 33, 1189 (1974), Phys. Rev. A12, 186 (1975)CrossRefGoogle Scholar
  13. 11.
    E.N. Lorenz, J. Atmo. Sci. 20, 130 (1963)CrossRefGoogle Scholar
  14. 12.
    R. Thom “Modèle mathématique de la morphogénèse”, 10–18, Paris (1974)Google Scholar
  15. 13.
    A. Andronov and L. Pontryagin, Dokl. Akad. Nauk. SSSR 14, 247 (1937)Google Scholar
  16. 14.
    D. Ruelle, in “Turbulence and Navier-Stokes equation” Lecture Notes in Math, 565, Springer Verlag, Berlin (1975)Google Scholar
  17. 14a.
    O. Lanford, III lectures at IHES (1975)Google Scholar
  18. 14b.
    R.B. Williams “On the Structure of the Lorenz Attractors”, preprintGoogle Scholar
  19. 15.
    V. Arnold, A. Avez, “Ergodic Problems of Classical Mechanics”, Benjamin, New York (1969)Google Scholar
  20. 16.
    R. Betchov and W.O. Criminale Jr. “Stability of Parallel Flows”, Acad. Press, New York (1966)Google Scholar
  21. 17.
    Landau et Lifchitz, “Mécanique des Fluides” chap. III, §27, ed. Mir. (Moscou) (1971)Google Scholar
  22. 18.
    D.R. Caldwell. J. of Fluid Mech. 64, 347 (1974)Google Scholar
  23. 19.
    N.N. Bogoliubov, J.A. Mitropolskii, A.M. Samoilenko, “Methods of accelerated convergence in non linear mechanics” Spinger Verlag, Berlin (1976)Google Scholar
  24. 20.
    V.I. Arnold, Small divisors I, Izv. Akad. Nauk. SSSR Ser. Mat. 25 (1), 21 (1961),Small divisors II, Usp. Mat. Nauk 18 (5), 13 (1963); 18 (6), 91 (1963)Google Scholar
  25. 20a.
    M.R. Hermann, Thesis, Orsay (1976)Google Scholar
  26. 21.
    Reference 19, p. 154Google Scholar
  27. 22.
    Reference 9, p. 788Google Scholar
  28. 22a.
    M. Shub, Thesis, Univ. of Calif. Berkeley (1967)Google Scholar
  29. 23.
    J.P. Gollub, S.L. Hulbert, G.M. Dolny and H.L. Swinney, to appear in “Photon correlation, spectroscopy and velocimetry” Ed. E.R. Pyke and H.Z. Cummins, Plenum Press (1976)Google Scholar
  30. 24.
    J.L. Ibanez, Y. Pomeau, to be publishedGoogle Scholar
  31. 25.
    Ref. 3, and P. Stefan, preprint IHES (Bures-sur-Yvette) Dec. 1976, A.N. Šarkovskiy, Urk. Math. t. 16, 1 (1964), B. Derrida and Y. Pomeau, to be publishedCrossRefPubMedGoogle Scholar

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • Y. Pomeau
    • 1
  1. 1.CEA, DPhTFrance

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