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

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Abstract

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 Maé at the International Congress of Mathematicians in 1983. The main technical novelty is a probabilistic method for the construction of perturbations, using random walks.

Original languageEnglish (US)
Pages (from-to)49-93
Number of pages45
JournalJournal of the Institute of Mathematics of Jussieu
Volume9
Issue number1
DOIs
StatePublished - Jan 2010

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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