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symplectic diffeomorphisms

Journal of the Institute of Mathematics of Jussieu (1)

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C1-generic symplectic diffeomorphisms: partial hyperbolicity and zero centre Lyapunov exponents
Part of
- Dynamical systems with hyperbolic behavior
Jairo Bochi
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 9 / Issue 1 / January 2010

Published online by Cambridge University Press:

26 March 2009, pp. 49-93

Print publication:

January 2010
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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.