Partial hyperbolicity for symplectic diffeomorphisms

By A. Tahzibi, Vanderlei Horita. 2004

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We prove that every robustly transitive and every stably ergodic symplectic diffeomorphism on a compact manifold admits a dominated splitting. In fact, these diffeomorphisms are partially hyperbolic.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1cbe1be99e869205ed79ec9acbb1febec0a37a8e