Nonlocally maximal and premaximal hyperbolic sets
Dynamical Systems
2015-10-21 v1
Abstract
We prove that for any closed manifold of dimension 3 or greater that there is an open set of smooth flows that have a hyperbolic set that is not contained in a locally maximal one. Additionally, we show that the stabilization of the shadowing closure of a hyperbolic set is an intrinsic property for premaximality. Lastly,we review some results due to Anosov that concern premaximality.
Cite
@article{arxiv.1510.05933,
title = {Nonlocally maximal and premaximal hyperbolic sets},
author = {T. Fisher and T. Petty and S. Tikhomirov},
journal= {arXiv preprint arXiv:1510.05933},
year = {2015}
}
Comments
25 pages, 4 figures