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Hopf Bifurcation for Invariant Tori

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Dynamical Systems

Part of the book series: Progress in Mathematics ((PM,volume 8))

Abstract

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.].

Slightly expanded version of a conference given at the Bressanone CIME session on dynamical systems, June 1978.

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Bibliography

  1. R. Bowen, A model for Couette flow data, in Berkeley turbulence seminar, Lect.Notes in Math 615, Springer Verlag, Berlin 1977.

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  2. A. Chenciner, G. Iooss, Bifurcations de tores invariants, to appear in Archives of rational mechanics and analysis, 1979.

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  3. A. Chenciner, G. Iooss, Persistance et Bifurcation de tores invariants, to appear.

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  4. J.H. Curry, J.A. Yorke, A transition from Hopf bifurcation to chaos: computer experiments with maps on J. Preprint 1978.

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  5. M.R. Herman, Mesure de Lebesgue et nombre de rotation, in Lect. Notes in Math, 597, Springer Verlag, Berlin 1977, p.271, 293.

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  6. M.W. Hirsch, C.C. Pugh, M. Shub, Invariant manifolds, Lect. Notes in Math. 583, Springer Verlag, Berlin 1977.

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  7. 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).

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  8. D. Ruelle, F. Takens, On the nature of turbulence.Comm.Math. Phys.20,p.167–192 (1971).

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Authors and Affiliations

  1. I.M.S.P. Mathematics Dept. Parc Valrose, 06034, Nice Cedex, France

    A. Chenciner

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  1. A. Chenciner
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C. Marchioro

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© 1980 Springer-Verlag Berlin Heidelberg

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Chenciner, A. (1980). Hopf Bifurcation for Invariant Tori. In: Marchioro, C. (eds) Dynamical Systems. Progress in Mathematics, vol 8. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4899-3743-8_4

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  • DOI: https://doi.org/10.1007/978-1-4899-3743-8_4

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-0-8176-3024-9

  • Online ISBN: 978-1-4899-3743-8

  • eBook Packages: Springer Book Archive

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