English

On the growth rate of periodic orbits for vector fields

Dynamical Systems 2017-09-21 v1

Abstract

We establish the relationship between the growth rate of periodic orbits and the topological entropy for C1C^1 generic vector fields: this extends a classical result of Katok for C1+α(α>0)C^{1+\alpha}(\alpha>0) surface diffeomorphisms to C1C^1 generic vector fields of any dimension. The main difficulty comes from the existence of singularities and the shear of the flow.

Keywords

Cite

@article{arxiv.1709.06717,
  title  = {On the growth rate of periodic orbits for vector fields},
  author = {Wanlou Wu and Dawei Yang and Yong Zhang},
  journal= {arXiv preprint arXiv:1709.06717},
  year   = {2017}
}