Stable manifolds and the Perron-Irwin method

Ergodic Theory and Dynamical Systems

Volumn 24, Issue 5, 2004, Pages 1359-1394

  Chaperon, Marc ^a  

^a INSTITUT DE MATHÉMATIQUES DE JUSSIEU   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 9344233816     PISSN: 01433857     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0143385703000701     Document Type: Article

References (21)

1. M. Chaperon. Géométrie différentielle et singularités de systèmes dynamiques. Astérisque 138-139 (1986).
2. k-conjugacy of holomorphic flows near a singularity. Publ. Math. Inst. Hautes Études Sci. 64 (1987), 143-183.
3. M. Chaperon. Variétés stables et formes normales. C. R. Acad. Sci. Paris 317, Série 1 (1993), 87-92.
4. M. Chaperon. Invariant manifolds revisited. Proceedings of the Steklov Institute 236 (2002), 415-433.
5. M. Chaperon. Invariant manifolds and semi-conjugacies. To appear.
6. M. Chaperon and F. Coudray. Invariant manifolds, conjugacies and blow-up. Ergod. Th. & Dynam. Sys. 17 (1997), 783-791.
7. A. Chenciner. Bifurcations de points fixes elliptiques: Courbes invariantes. Publ. Math. Inst. Hautes Études Sci. 61 (1985), 67-127. A. Chenciner. Orbites périodiques et ensembles de Cantor invariants. Invent. Math. 80 (1985), 81-106. A. Chenciner. Orbites périodiques de 'petites' périodes et élimination résonnante des couples de courbes invariantes. Publ. Math. Inst. Hautes Études Sci. 66 (1988), 5-91.
8. A. Chenciner. Bifurcations de points fixes elliptiques: Courbes invariantes. Publ. Math. Inst. Hautes Études Sci. 61 (1985), 67-127. A. Chenciner. Orbites périodiques et ensembles de Cantor invariants. Invent. Math. 80 (1985), 81-106. A. Chenciner. Orbites périodiques de 'petites' périodes et élimination résonnante des couples de courbes invariantes. Publ. Math. Inst. Hautes Études Sci. 66 (1988), 5-91.
9. A. Chenciner. Bifurcations de points fixes elliptiques: Courbes invariantes. Publ. Math. Inst. Hautes Études Sci. 61 (1985), 67-127. A. Chenciner. Orbites périodiques et ensembles de Cantor invariants. Invent. Math. 80 (1985), 81-106. A. Chenciner. Orbites périodiques de 'petites' périodes et élimination résonnante des couples de courbes invariantes. Publ. Math. Inst. Hautes Études Sci. 66 (1988), 5-91.
10. A. Chenciner and G. Ioos. Bifurcations de tores invariants. Arch. Rational Mech. Anal. 69 (1979), 109-198.
11. C. Conley and E. Zehnder. The Birkhoff-Lewis fixed point theorem and a conjecture of V. I. Arnol'd. Invent. Math. 73 (1983), 33-49.
12. R. de la Llave and C. Eugene Wayne. On Irwin's proof of the pseudostable manifold theorem. Math. Z. 219 (1995), 301-321.
13. N. Fenichel. Persistence and smoothness of invariant manifolds for flows. Ind. Univ. Math. J. 21 (1971), 193-225.
14. M. W. Hirsch, C. C. Pugh and M. Shub. Invariant Manifolds (Springer Lecture Notes in Mathematics, 583). Springer, Berlin, 1977.
15. M. C. Irwin. Smooth Dynamical Systems. Academic Press, London, 1980.
16. M. C. Irwin. A new proof of the pseudo-stable manifold theorem. J. London Math. Soc. 21 (1980), 557-566.
17. R. McGehee. The stable manifold theorem via an isolating block. Symposium on Ordinary Differential Equations (Springer Lecture Notes in Mathematics, 312). Springer, Berlin, 1973, pp. 194-217.
18. P. D. McSwiggen. An inverse function theorem with application to dynamical systems. J. Diff. Eqs 118 (1995), 194-217.
19. D. Ruelle and F. Takens. On the nature of turbulence. Comm. Math. Phys. 20 (1971), 167-192.
20. S. Sternberg. Local contractions and a theorem of Poincaré. Amer. J. Math. 79 (1957), 809-824.
21. S. Sternberg. On the structure of local homeomorphisms of Euclidean n-space II. Amer. J. Math. 80 (1958), 623-631.