Oriented shadowing property and $\Omega$-stability for vector fields

Shaobo Gan; Ming Li; Sergey B. Tikhomirov

Oriented shadowing property and $\Omega$-stability for vector fields

Dynamical Systems 2014-08-12 v2

Authors: Shaobo Gan , Ming Li , Sergey B. Tikhomirov

Abstract

We call that a vector field has the oriented shadowing property if for any $\varepsilon>0$ there is $d>0$ such that each $d$ -pseudo orbit is $\varepsilon$ -oriented shadowed by some real orbit. In this paper, we show that the $C^1$ -interior of the set of vector fields with the oriented shadowing property is contained in the set of vector fields with the $\Omega$ -stability.

Keywords

shadowing property vector fields

Cite

@article{arxiv.1404.3545,
  title  = {Oriented shadowing property and $\Omega$-stability for vector fields},
  author = {Shaobo Gan and Ming Li and Sergey B. Tikhomirov},
  journal= {arXiv preprint arXiv:1404.3545},
  year   = {2014}
}

Oriented shadowing property and $\Omega$-stability for vector fields

Abstract

Keywords

Cite

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