On the Density of Periodic Measures for Star Vector Fields
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917250730033152 |
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| author | Sun, Qimai Wang, Guangwa Wu, Wanlou |
| author_facet | Sun, Qimai Wang, Guangwa Wu, Wanlou |
| contents | 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 $C^{1+α}(α>0)$ diffeomorphisms to $C^1$ star vector field of any dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_05402 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Density of Periodic Measures for Star Vector Fields Sun, Qimai Wang, Guangwa Wu, Wanlou Dynamical Systems 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 $C^{1+α}(α>0)$ diffeomorphisms to $C^1$ star vector field of any dimension. |
| title | On the Density of Periodic Measures for Star Vector Fields |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2602.05402 |