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arXiv · 2006.16602

Denjoy sub-systems and horseshoes

Marie-Claude Arnaud
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Abstract

We introduce a notion of weak Denjoy subsystem (WDS) that generalizes the Aubry-Mather Cantor sets to diffeomorphisms of manifolds. We explain how a rotation number can be associated to such a WDS. Then we build in any horseshoe a continuous one parameter family of such WDS that is indexed by its rotation number. Looking at the inverse problem in the setting of Aubry-Mather theory, we also prove that for a generic conservative twist map of the annulus, the majority of the Aubry-Mather sets are contained in some horseshoe that is associated to a Aubry-Mather set with a rational rotation number.

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Marie-Claude Arnaud. 2020-06-30. Denjoy sub-systems and horseshoes. https://arxiv.org/abs/2006.16602

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