[Les flots géodésiques partiellement hyperboliques sont Anosov]
Considérons une action de ou 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 or -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.
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Publié le :
Gonzalo Contreras 1
@article{CRMATH_2002__334_7_585_0, author = {Gonzalo Contreras}, title = {Partially hyperbolic geodesic flows are {Anosov}}, journal = {Comptes Rendus. Math\'ematique}, pages = {585--590}, publisher = {Elsevier}, volume = {334}, number = {7}, year = {2002}, doi = {10.1016/S1631-073X(02)02196-9}, language = {en}, }
Gonzalo Contreras. Partially hyperbolic geodesic flows are Anosov. Comptes Rendus. Mathématique, Volume 334 (2002) no. 7, pp. 585-590. doi : 10.1016/S1631-073X(02)02196-9. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02196-9/
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