On the singular hyperbolicity of star flows
Dynamical Systems
2014-08-28 v2
Abstract
We prove for a generic star vector field that, if for every chain recurrent class of all singularities in have the same index, then the chain recurrent set of is singular hyperbolic. We also prove that every Lyapunov stable chain recurrent class of is singular hyperbolic. As a corollary, we prove that the chain recurrent set of a generic 4-dimensional star flow is singular hyperbolic.
Cite
@article{arxiv.1310.8118,
title = {On the singular hyperbolicity of star flows},
author = {Yi Shi and Shaobo Gan and Lan Wen},
journal= {arXiv preprint arXiv:1310.8118},
year = {2014}
}
Comments
29 pages, version to appear in J. Mod. Dyn