no. 21-22
Dynamical Systems/Ordinary Differential Equations
Invariant manifold theory via generating maps
[Applications génératrices et variétés invariantes]

Présenté par : Étienne Ghys

Chaperon, Marc1
1 Institut de mathématiques de Jussieu & Université Paris 7, UFR de mathématiques, site Chevaleret, case 7012, 75205 Paris cedex 13, France
Comptes Rendus. Mathématique, Tome 346 (2008) no. 21-22, pp. 1175-1180.

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

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

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.09.030
Chaperon, Marc 1

1 Institut de mathématiques de Jussieu & Université Paris 7, UFR de mathématiques, site Chevaleret, case 7012, 75205 Paris cedex 13, France 
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Chaperon, Marc. Invariant manifold theory via generating maps. Comptes Rendus. Mathématique, Tome 346 (2008) no. 21-22, pp. 1175-1180. doi : 10.1016/j.crma.2008.09.030. http://archive.numdam.org/articles/10.1016/j.crma.2008.09.030/

[1] Chaperon, M., Ergodic Theory Dynam. Systems (Fathi, A.; Yoccoz, J.-C., eds.) (Dynamical Systems: Michael Herman Memorial Volume), Volume 24, Cambridge University Press, 2004, pp. 1359-1394

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

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

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

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

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