Comptes Rendus
Dynamical Systems
Stable products of spheres in the non-linear coupling of oscillators or quasi-periodic motions
Comptes Rendus. Mathématique, Volume 339 (2004) no. 9, pp. 625-629.

For generic families of vector fields or transformations, normally hyperbolic invariant products of spheres appear near partially elliptic rest points.

Pour les familles génériques de champs de vecteurs ou de transformations, toutes sortes de produits de sphères normalement hyperboliques peuvent apparaître près des points stationnaires partiellement elliptiques.

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Accepted:
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DOI: 10.1016/j.crma.2004.09.017
Mathilde Kammerer-Colin de Verdière 1

1 Université de Bourgogne, laboratoire de topologie, UMR 5584 du CNRS, B.P. 47870, 21078 Dijon cedex, France
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Mathilde Kammerer-Colin de Verdière. Stable products of spheres in the non-linear coupling of oscillators or quasi-periodic motions. Comptes Rendus. Mathématique, Volume 339 (2004) no. 9, pp. 625-629. doi : 10.1016/j.crma.2004.09.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.09.017/

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[2] M. Chaperon Some results on stable manifolds, C. R. Acad. Sci. Paris, Ser. I, Volume 333 (2001), pp. 119-124

[3] M. Chaperon, Stable manifolds and the Perron–Irwin method, Ergodic Theory Dyn. Systems, volume in memory of M.R. Herman, in press

[4] A. Chenciner Bifurcations de points fixes elliptiques I. Courbes invariantes, Inst. Hautes Études Sci. Publ. Math., Volume 61 (1985), pp. 67-127

[5] N. Fenichel Persistence and smoothness of invariant manifolds for flows, Indiana Univ. Math. J., Volume 21 (1971), pp. 193-225

[6] J. Guckenheimer; P. Holmes Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Appl. Math. Sci., vol. 42, Springer-Verlag, 1983

[7] M.W. Hirsch; C.C. Pugh; M. Shub Invariant Manifolds, Lecture Notes in Math., vol. 583, Springer-Verlag, 1977

[8] M. Kammerer-Colin de Verdière, Generalized Hopf bifurcations, in preparation

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