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Comptes Rendus Mathématique
Volume 334, n° 7
pages 585-590 (2002)
Doi : S1631-073X(02)02196-9
Received : 30 October 2001 ;  accepted : 5 November 2001
Partially hyperbolic geodesic flows are Anosov
Les flots géodésiques partiellement hyperboliques sont Anosov
 

Gonzalo Contreras
Cimat, PO box 402, 36.000 Guanajuato GTO, México, Mexique 

Note presented by Etienne Ghys

Abstract

We prove that if a Z or R-action by symplectic linear maps on a symplectic vector bundle E has a weakly dominated invariant splitting E =S U with dimU =dimS , then the action is hyperbolic. In particular, contact and geodesic flows with a dominated splitting with dimS =dimU are Anosov. To cite this article: G. Contreras, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 585-590.

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

Considérons une action de R ou Z sur un fibré vectoriel muni d'une struture symplectique par des applications linéaires préservant cette structure symplectique, et supposons que cette action possède une décomposition invariante faiblement dominée E =S U avec dimU =dimS . On montre alors que cette action est nécessairement hyperbolique. Pour citer cet article : G. Contreras, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 585-590.

The full text of this article is available in PDF format.
  Partially supported by CONACYT-México grant # 36496-E.


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