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Partial hyperbolicity for symplectic diffeomorphisms. (English) Zbl 1130.37356

Summary: 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.

MSC:

37D30 Partially hyperbolic systems and dominated splittings
37J10 Symplectic mappings, fixed points (dynamical systems) (MSC2010)
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References:

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