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Comptes Rendus Mathématique
Volume 337, n° 12
pages 791-796 (décembre 2003)
Doi : 10.1016/j.crma.2003.10.001
Received : 19 June 2003 ;  accepted : 4 October 2003
Flots robustement transitifs sur les variétés compactes
Robustly transitive flows on compact manifolds

Thérèse  Vivier
Université de Bourgogne, institut mathématiques de Bourgogne, CNRS-UMR 5584, UFR sciences et techniques, bâtiment Mirande, 9, avenue Alain Savary, BP 47 870, 21078 Dijon cedex, France 

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L'objet de cette Note est de présenter une preuve du résultat suivant : un champ de vecteurs   robustement transitif sur une variété compacte n'admet aucune singularité. On montre tout d'abord l'incompatibilité d'une décomposition dominée avec la présence de singularités hyperboliques selles. On prouve ensuite que la robuste transitivité implique l'existence d'une décomposition dominée. Pour citer cet article : T. Vivier, C. R. Acad. Sci. Paris, Ser. I 337 (2003).

Abstract

In this Note, we present a proof of the following result: robustly transitive  -vector fields on compact manifold admit no singularity. We first prove the incompatibility of dominated structure with hyperbolic saddles. Secondly, we show that robust transitivity implies the existence of dominated structure. To cite this article: T. Vivier, C. R. Acad. Sci. Paris, Ser. I 337 (2003).




© 2003  Académie des sciences@@#104156@@

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