JournalsaihpcVol. 23, No. 5pp. 641–661

Partial hyperbolicity for symplectic diffeomorphisms

  • Ali Tahzibi

    Departamento de Matemática e de Computação, ICMC/USP, Av. Trabalhador São Carlense, 400-Cx. Postal 668, 13560-320 São Carlos, SP, Brazil

  • Vanderlei Horita

    UNESP – Universidade Estadual Paulista, Departamento de Matemática, IBILCE, Rua Cristóvão Colombo 2265, 15054-000 S. J. Rio Preto, SP, Brazil
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Abstract

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. 641–661

DOI 10.1016/J.ANIHPC.2005.06.002