Invariant manifold theory via generating maps

Marc Chaperon

doi:10.1016/j.crma.2008.09.030

Dynamical Systems/Ordinary Differential Equations

Invariant manifold theory via generating maps

Presented by: Étienne Ghys

Marc Chaperon ¹

¹ Institut 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.

Abstract
Résumé

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: 2008-05-21
Accepted: 2008-09-29
Published online: 2008-10-16

DOI: 10.1016/j.crma.2008.09.030

Author's affiliations:

Marc Chaperon 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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     author = {Marc Chaperon},
     title = {Invariant manifold theory via generating maps},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1175--1180},
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     year = {2008},
     doi = {10.1016/j.crma.2008.09.030},
     language = {en},
}

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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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.09.030/

References
Cited by

[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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