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arXiv · 1709.06717

On the growth rate of periodic orbits for vector fields

Wanlou Wu·Dawei Yang·Yong Zhang
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Abstract

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

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Wanlou Wu, Dawei Yang, Yong Zhang. 2017-09-20. On the growth rate of periodic orbits for vector fields. https://arxiv.org/abs/1709.06717

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