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 generic vector fields: this extends a classical result of Katok for surface diffeomorphisms to 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}
}