Some topics about the transition to turbulence

  • P. Bergé
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 164)


The basic concepts allowing to define the different states of a dynamical system are illustrated through the behaviour of the Rayleigh-Bénard convection in confined geometry. The interest of the Poincaré sections of the phase space is pointed out in parallel with that of the iterated maps. Finally one shows how the deterministic chaos can be understood, thanks to the concepts of strange attractor.


Phase Space Strange Attractor Stable Limit Cycle Deterministic Chaos Periodic Regime 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    L.D. Landau and E.M. Lifshitz “Fluid Mechanics”, Pergamon Press, London 1959.Google Scholar
  2. [2]
    D. Ruelle and F. Takens, Comm. Math. Phys. 20, 167 (1971).Google Scholar
  3. [3]
    P. Bergé and M. Dubois “Systems far from Equilibrium” Sitges 1980, Pringer-Verlag ed. by L. Garrido, p. 381.Google Scholar
  4. [4]
    P. Bergé “chaos and order in nature” Schloss Elman 1981, Springer-Verlag ed. by H. Haken p.14.Google Scholar
  5. [5]
    P. Bergé and M. Dubois, J. Physique Lettres 40, L505 (1979).Google Scholar
  6. [6]
    M. Dubois and P. Bergé, Phys. Letters A76, 53 (1980)Google Scholar
  7. [7]
    M. Dubois, this volume and M. Dubois, P. Bergé and V. Croquette, Comptes Rendus Acad. Sci Paris, Sept. 1981.Google Scholar
  8. [8]
    E. Lorenz, J. Atmos. Sci 20, 130 (1963).Google Scholar
  9. [9]
    P. Collet, J.P. Eckmann “Iterated mans on the interval as dynamical systems” P. Ph. ed. A. Jaffe, D. Ruelle, Birkhaüser 1980.Google Scholar
  10. [10]
    M.G. Velarde in “Non Linear Phenomena at Phase Transitions and Instabilities” NATO Advanced Study Institute, Norway (1981).Google Scholar
  11. [11]
    M. Dubois in “Symmetries and Broken Symmetries in Condensed Matter Physics” ed. by N. Boccara (IDSET Paris) 1981.Google Scholar
  12. [12]
    M. Dubois and P. Bergé, J. Physique 42, 167 (1981).Google Scholar
  13. [13]
    P. Bergé, M. Dubois and V. Croquette “Convective Transport and Instability Phenomena” Euromech 138, Karlsrule 1981 ed. by H. Oertel and J. Zferep.Google Scholar
  14. [14]
    M. Renon, Commun. Math. Phys. 50, 69–77 (1976).Google Scholar
  15. [15]
    O.E. Rossler, Phys. Letters A57, 397 (1976).Google Scholar
  16. [16]
    P. Manneville and Y. Pomeau, Phys. Letters 75A, 1 (1979).Google Scholar
  17. [17]
    P. Bergé, M. Dubois, P. Manneville and Y. Pomeau, J. Physique Lettres 41, L341 (1980).Google Scholar
  18. [18]
    M.J. Feigenbaum, Phys. Letters 74A, 375 (1979).Google Scholar
  19. [19]
    J. Maurer and A. Libchaber, J. Physique Lettres 41, L515 (1980).Google Scholar
  20. [20]
    M. Giglio, S. Musaggi and U. Perini, to be published.Google Scholar
  21. [21]
    R. Shaw, Z. Naturforsch 36a, 80 (1981).Google Scholar
  22. [22]
    A. Arneodo, P. Coullet and C. Tresser, Phys. Letters 79A, 259 (1980).Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • P. Bergé
    • 1
  1. 1.Service de Physique du Solide et de Résonance Magnétique CEN-SaclayGif-sur-Yvette CedexFrance

Personalised recommendations