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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.23605 |
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| _version_ | 1866918108562718720 |
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| author | Lu, Yuansheng Wu, Wanlou |
| author_facet | Lu, Yuansheng Wu, Wanlou |
| contents | In this paper, we proved that for every $C^1$ star vector fields on three-dimensional manifolds, every ergodic hyperbolic invariant measure which is not supported on singularities can be approximated by periodic measures, and the Lyapunov exponents of the ergodic hyperbolic invariant measure can also be approximated by the Lyapunov exponents of those periodic measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23605 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Lyapunov Exponents of Hyperbolic Measures for $C^1$ Star Vector Fields on Three-dimensional Manifolds Lu, Yuansheng Wu, Wanlou Dynamical Systems In this paper, we proved that for every $C^1$ star vector fields on three-dimensional manifolds, every ergodic hyperbolic invariant measure which is not supported on singularities can be approximated by periodic measures, and the Lyapunov exponents of the ergodic hyperbolic invariant measure can also be approximated by the Lyapunov exponents of those periodic measures. |
| title | The Lyapunov Exponents of Hyperbolic Measures for $C^1$ Star Vector Fields on Three-dimensional Manifolds |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2507.23605 |