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DENJOY SUB-SYSTEMS AND HORSESHOES

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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Dates and versions

hal-02884320 , version 1 (29-06-2020)

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Marie-Claude Arnaud. DENJOY SUB-SYSTEMS AND HORSESHOES. 2020. ⟨hal-02884320⟩
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