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arXiv · 2602.05402

On the Density of Periodic Measures for Star Vector Fields

Qimai Sun·Guangwa Wang·Wanlou Wu
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Abstract

In this paper, we prove that every ergodic hyperbolic invariant measure of a $C^1$ star vector field can be approximated by periodic measures in weak$^*$ topology. This extends a classical result of Katok \cite{Ka} for $C^{1+\alpha}(\alpha>0)$ diffeomorphisms to $C^1$ star vector field of any dimension.

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Qimai Sun, Guangwa Wang, Wanlou Wu. 2026-02-05. On the Density of Periodic Measures for Star Vector Fields. https://arxiv.org/abs/2602.05402

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