Comptes Rendus
no. 21-22
Dynamical Systems/Ordinary Differential Equations
Invariant manifold theory via generating maps
Étienne Ghys
Marc Chaperon1
1Institut de mathématiques de Jussieu & Université Paris 7, UFR de mathématiques, site Chevaleret, case 7012, 75205 Paris cedex 13, France
Comptes Rendus. Mathématique, Volume 346 (2008) no. 21-22, pp. 1175-1180

We present a synthetic approach to invariant manifold theorems, based upon the notion of a generating map.

Nous présentons une approche synthétique de la théorie des variétés invariantes, fondée sur la notion d'application génératrice.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.09.030

Marc Chaperon  1

1 Institut de mathématiques de Jussieu & Université Paris 7, UFR de mathématiques, site Chevaleret, case 7012, 75205 Paris cedex 13, France 
Marc Chaperon. Invariant manifold theory via generating maps. Comptes Rendus. Mathématique, Volume 346 (2008) no. 21-22, pp. 1175-1180. doi: 10.1016/j.crma.2008.09.030
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[1] M. Chaperon, Ergodic Theory Dynam. Systems (A. Fathi; J.-C. Yoccoz, eds.) (Dynamical Systems: Michael Herman Memorial Volume), Volume 24, Cambridge University Press, 2004, pp. 1359-1394

[2] M. Chaperon The Lipschitzian core of some invariant manifold theorems, Ergodic Theory Dynam. Systems, Volume 28 (2008), pp. 1419-1441

[3] M. Chaperon, S. López de Medrano, Invariant manifolds and semi-conjugacies, in preparation

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

[5] M. Gromov Metric Structures for Riemannian and Non-Riemannian Spaces, Birkhäuser, 1999

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

[7] R. McGehee; E.A. Sander A new proof of the stable manifold theorem, Z. Angew. Math. Phys., Volume 47 (1996) no. 4, pp. 497-513

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