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C1-generic symplectic diffeomorphisms: partial hyperbolicity and zero centre Lyapunov exponents

  • Jairo Bochi (a1)


We prove that if f is a C1-generic symplectic diffeomorphism then the Oseledets splitting along almost every orbit is either trivial or partially hyperbolic. In addition, if f is not Anosov then all the exponents in the centre bundle vanish. This establishes in full a result announced by Mañé at the International Congress of Mathematicians in 1983. The main technical novelty is a probabilistic method for the construction of perturbations, using random walks.



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C1-generic symplectic diffeomorphisms: partial hyperbolicity and zero centre Lyapunov exponents

  • Jairo Bochi (a1)


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