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Denjoy sub-systems and horseshoes
- Publication Year :
- 2020
-
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.
- Subjects :
- Mathematics - Dynamical Systems
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2006.16602
- Document Type :
- Working Paper