Sectional connecting lemma
Dynamical Systems
2018-04-03 v1
Abstract
A hyperbolic set on a compact manifold M, satisfies the property: given two of your any points p and q, such that for all positive \epsilon>0, there is a trajectory in the hyperbolic set from a point \epsilon-close to p to a point \epsilon-close to q, then there is a point in M whose \alpha-limit is that of p and whose \omega-limit is that of q. Bautista and Morales give a version of this property, for sectional-Anosov flows (vector fields whose maximal invariant set is sectional-hyperbolic), including some conditions; among them that limit the dimension of M to three. In this paper, we prove a generalization of this result, for sectional-hyperbolic sets of codimension one in high dimensions.
Cite
@article{arxiv.1804.00646,
title = {Sectional connecting lemma},
author = {Serafin Bautista and Valdiane Sales and Yeison Sánchez},
journal= {arXiv preprint arXiv:1804.00646},
year = {2018}
}