Hopf Bifurcation for Invariant Tori

  • A. Chenciner
Part of the Progress in Mathematics book series (PM, volume 8)


I want to describe some joint work with Gérard IOOSS of Nice University connected with the Ruelle and Takens deterministic approach to turbulence. The main references are [R.T.], [C.I.1.], [C.I.2.].


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  1. [B]
    R. Bowen, A model for Couette flow data, in Berkeley turbulence seminar, Lect.Notes in Math 615, Springer Verlag, Berlin 1977.Google Scholar
  2. [C.I.1.]
    A. Chenciner, G. Iooss, Bifurcations de tores invariants, to appear in Archives of rational mechanics and analysis, 1979.Google Scholar
  3. [C.I.2.]
    A. Chenciner, G. Iooss, Persistance et Bifurcation de tores invariants, to appear.Google Scholar
  4. [C.Y.]
    J.H. Curry, J.A. Yorke, A transition from Hopf bifurcation to chaos: computer experiments with maps on J. Preprint 1978.Google Scholar
  5. [H]
    M.R. Herman, Mesure de Lebesgue et nombre de rotation, in Lect. Notes in Math, 597, Springer Verlag, Berlin 1977, p.271, 293.Google Scholar
  6. [H.P.S.]
    M.W. Hirsch, C.C. Pugh, M. Shub, Invariant manifolds, Lect. Notes in Math. 583, Springer Verlag, Berlin 1977.Google Scholar
  7. [I.]
    G. Iooss, Sur la deuxième bifurcation d’une solution stationnaire de systèmes du type Navier-Stokes. Arch.Rat.Mech.Anal. 64,4, p.339–369 (1977).CrossRefGoogle Scholar
  8. [R.T.]
    D. Ruelle, F. Takens, On the nature of turbulence.Comm.Math. Phys.20,p.167–192 (1971).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1980

Authors and Affiliations

  • A. Chenciner
    • 1
  1. 1.I.M.S.P. Mathematics Dept. Parc ValroseNice CedexFrance

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