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 dim U=dim S, then the action is hyperbolic. In particular, contact and geodesic flows with a dominated splitting with dim S=dim U are Anosov. To cite this article: G. Contreras, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 585–590.
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