Homoclinic classes for generic C^1 vector fields
Dynamical Systems
2007-05-23 v1
Abstract
We prove that homoclinic classes for a residual set of C^1 vector fields X on closed n-manifolds are maximal transitive and depend continuously on periodic orbit data. In addition, X does not exhibit cycles formed by homoclinic classes. We also prove that a homoclinic class of X is isolated if and only if it is Omega-isolated, and that it is the intersection of its stable set and its unstable set. All these properties are well known for structurally stable Axiom A vector fields.
Keywords
Cite
@article{arxiv.math/0108226,
title = {Homoclinic classes for generic C^1 vector fields},
author = {C. M. Carballo and C. A. Morales and M. J. Pacifico},
journal= {arXiv preprint arXiv:math/0108226},
year = {2007}
}
Comments
17 pages