On a theorem of Philip Hartman

Brahim Abbaci

doi:10.1016/j.crma.2004.10.010

Dynamical Systems

On a theorem of Philip Hartman

Presented by: Étienne Ghys

Brahim Abbaci ¹

¹ Universite des sciences et de la technologie Houari Boumédienne, faculté de mathématiques, BP 32, EL ALIA Bab Ezzouar, 16111 Alger, Algeria

Comptes Rendus. Mathématique, Volume 339 (2004) no. 11, pp. 781-786

Abstract (Original language)
Résumé

We generalize Hartman's $C^{1}$ linearization theorem for local contractions and explain how to simplify its proof.

Nous généralisons le théorème de linéarisation $C^{1}$ des contractions locales dû à Hartman et expliquons comment en simplifier la démonstration.

Received: 2004-07-08
Accepted: 2004-10-03
Published online: 2004-11-10

DOI: 10.1016/j.crma.2004.10.010

Author's affiliations:

Brahim Abbaci ¹

¹ Universite des sciences et de la technologie Houari Boumédienne, faculté de mathématiques, BP 32, EL ALIA Bab Ezzouar, 16111 Alger, Algeria

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Brahim Abbaci. On a theorem of Philip Hartman. Comptes Rendus. Mathématique, Volume 339 (2004) no. 11, pp. 781-786. doi: 10.1016/j.crma.2004.10.010

References
Cited by

[1] B. Abbaci, Variétés invariantes et applications, Thèse, Université Paris 7, 2001

[2] B. Abbaci, A generalization of a theorem by Hartman and some applications, in preparation

[3] M. Chaperon Variétés stables et formes normales, C. R. Acad. Sci. Paris, Ser. I, Volume 317 (1993), pp. 87-92

[4] M. Chaperon Invariant manifolds revisited, Proc. Steklov Instit., Volume 236 (2002), pp. 415-433

[5] M. Chaperon, Stable manifolds and the Perron–Irwin method, in: Ergodic Theory and Dynamical Systems in memory of Michael R. Herman, in press

[6] R. De La Llave; C.E. Wayne On Irwin's proof of the pseudo-stable manifold theorem, Math. Z., Volume 219 (1995), pp. 301-321

[7] P. Hartman On local homeomorphisms of Euclidean spaces, Bol. Soc. Mat. Mex., Volume 5 (1960), pp. 220-241

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