English

On the singular hyperbolicity of star flows

Dynamical Systems 2014-08-28 v2

Abstract

We prove for a generic star vector field XX that, if for every chain recurrent class CC of XX all singularities in CC have the same index, then the chain recurrent set of XX is singular hyperbolic. We also prove that every Lyapunov stable chain recurrent class of XX 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

R2 v1 2026-06-22T01:57:20.178Z