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Comptes Rendus Mathématique
Volume 341, n° 12
pages 755-759 (décembre 2005)
Doi : 10.1016/j.crma.2005.10.020
Received : 1 October 2005 ;  accepted : 19 October 2005
Extension of invariant manifolds and applications
Prolongement de variétés invariantes et applications
 

Brahim Abbaci
Université des sciences et de la technologie Houari-Boumèdiene, faculté de mathématiques, BP 32, El Alia, 16111 Alger, Algeria 

Abstract

We state an extension theorem for invariant manifolds of diffeomorphisms near a normally hyperbolic' invariant torus. We apply this result in particular to the resolution of equations   ( ) where the  ʼs are linear diagonal vector fields and the  ʼs are germs at 0 of smooth functions on  . To cite this article: B. Abbaci, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.
Résumé

Nous énonçons un théorème de prolongement de variété invariante et nous en donnons une application à la résolution des équations   ( ) où les   sont des champs de vecteurs linéaires diagonaux et les   des germes en 0 de fonctions   de   vérifiant certaines conditions. Pour citer cet article : B. Abbaci, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.


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