A C1 generic condition for existence of symbolic extensions of volume preserving diffeomorphisms

Details A C1 generic condition for existence of symbolic extensions of volume preserving diffeomorphisms A C1 generic condition for existence of symbolic extensions of volume preserving diffeomorphisms

2011-09-14

arxiv.org/abs/1109.3080v2

Mathematics

Dynamical Systems

Scientific paper

We prove that a C1-generic volume preserving diffeomorphism has a symbolic
extension if and only if this diffeomorphism is partial hyperbolic. This result
is obtained by means of good dichotomies. In particular, we prove Bonatti's
conjecture in the volume preserving scenario. More precisely, in the complement
of Anosov diffeomorphisms we have densely robust heterodimensional cycles.

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