Partially hyperbolic geodesic flows are Anosov
[Les flots géodésiques partiellement hyperboliques sont Anosov]
Contreras, Gonzalo1
1 Cimat, PO box 402, 36.000 Guanajuato GTO, México, Mexique
Comptes Rendus. Mathématique, Tome 334 (2002) no. 7, pp. 585-590.

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.

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.

Reçu le :
Accepté le :
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DOI : 10.1016/S1631-073X(02)02196-9
Contreras, Gonzalo 1

1 Cimat, PO box 402, 36.000 Guanajuato GTO, México, Mexique 
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Contreras, Gonzalo. Partially hyperbolic geodesic flows are Anosov. Comptes Rendus. Mathématique, Tome 334 (2002) no. 7, pp. 585-590. doi : 10.1016/S1631-073X(02)02196-9. http://archive.numdam.org/articles/10.1016/S1631-073X(02)02196-9/

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