Lyapunov spectrum of homoclinic classes
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911627876499456 |
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| author | Díaz, Lorenzo J. Gelfert, Katrin Wang, Xiaodong Yang, Jiagang |
| author_facet | Díaz, Lorenzo J. Gelfert, Katrin Wang, Xiaodong Yang, Jiagang |
| contents | We study the Lyapunov spectrum of the ergodic measures of isolated homoclinic classes of $C^1$-generic diffeomorphisms. We show that this spectrum has nonempty interior and that any vector in its interior is the spectrum of some ergodic measure fully supported on the homoclinic class. We also discuss the averaged Lyapunov spectrum of homoclinic classes (an extension of the Lyapunov graph). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25063 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lyapunov spectrum of homoclinic classes Díaz, Lorenzo J. Gelfert, Katrin Wang, Xiaodong Yang, Jiagang Dynamical Systems 37D25, 37D35, 37C40 We study the Lyapunov spectrum of the ergodic measures of isolated homoclinic classes of $C^1$-generic diffeomorphisms. We show that this spectrum has nonempty interior and that any vector in its interior is the spectrum of some ergodic measure fully supported on the homoclinic class. We also discuss the averaged Lyapunov spectrum of homoclinic classes (an extension of the Lyapunov graph). |
| title | Lyapunov spectrum of homoclinic classes |
| topic | Dynamical Systems 37D25, 37D35, 37C40 |
| url | https://arxiv.org/abs/2604.25063 |