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.
Cite this article
Ali Tahzibi, Vanderlei Horita, Partial hyperbolicity for symplectic diffeomorphisms. Ann. Inst. H. Poincaré Anal. Non Linéaire 23 (2006), no. 5, pp. 641–661DOI 10.1016/J.ANIHPC.2005.06.002