Constraints On Dynamics Preserving Certain Hyperbolic Sets
Dynamical Systems
2010-08-18 v2
Abstract
We establish two results under which the topology of a hyperbolic set constrains ambient dynamics. First if a set is a compact, transitive, expanding hyperbolic attractor of codimension 1 for some diffeomorphism, then it is a union of transitive, expanding attractors (or contracting repellers) of codimension 1 for any diffeomorphism such that it is hyperbolic. Secondly, if a set is a nonwandering, locally maximal, compact hyperbolic set for a surface diffeomorphism, then it is locally maximal for any diffeomorphism for which it is hyperbolic.
Cite
@article{arxiv.0906.5014,
title = {Constraints On Dynamics Preserving Certain Hyperbolic Sets},
author = {Aaron W. Brown},
journal= {arXiv preprint arXiv:0906.5014},
year = {2010}
}
Comments
19 pages