Denjoy sub-systems and horseshoes
Dynamical Systems
2020-07-01 v1
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.
Cite
@article{arxiv.2006.16602,
title = {Denjoy sub-systems and horseshoes},
author = {Marie-Claude Arnaud},
journal= {arXiv preprint arXiv:2006.16602},
year = {2020}
}