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arXiv · 1109.3080

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

Thiago Catalan
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Abstract

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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Thiago Catalan. 2012-03-27. A C1 generic condition for existence of symbolic extensions of volume preserving diffeomorphisms. https://doi.org/10.1088/0951-7715%2F25%2F12%2F3505

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