Lyapunov stable chain recurrence classes for singular flows

Shaobo Gan; Jiagang Yang; Rusong Zheng

Lyapunov stable chain recurrence classes for singular flows

Dynamical Systems 2024-11-21 v2

Authors: Shaobo Gan , Jiagang Yang , Rusong Zheng

Abstract

We show that for a $C^1$ generic vector field $X$ away from homoclinic tangencies, a nontrivial Lyapunov stable chain recurrence class is a homoclinic class. The proof uses an argument with $C^2$ vector fields approaching $X$ in $C^1$ topology, with their Gibbs $F$ -states converging to a Gibbs $F$ -state of $X$ .

Cite

@article{arxiv.2202.09742,
  title  = {Lyapunov stable chain recurrence classes for singular flows},
  author = {Shaobo Gan and Jiagang Yang and Rusong Zheng},
  journal= {arXiv preprint arXiv:2202.09742},
  year   = {2024}
}

Comments

63 pages, 3 figures

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