Finitness of measured homoclinic classes with large Lyapunov exponents for $\mathcal{C}^2$ surface diffeomorphisms
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916710324371456 |
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| author | Ghezal, Matéo |
| author_facet | Ghezal, Matéo |
| contents | We show the finiteness of homoclinic classes carrying measures with large Lyapunov exponents for $\mathcal{C}^2$ surface diffeomorphisms. As a consequence, we derive the finiteness of the set of ergodic measures of maximal entropy, in the case where the entropy of the system is large. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19908 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finitness of measured homoclinic classes with large Lyapunov exponents for $\mathcal{C}^2$ surface diffeomorphisms Ghezal, Matéo Dynamical Systems We show the finiteness of homoclinic classes carrying measures with large Lyapunov exponents for $\mathcal{C}^2$ surface diffeomorphisms. As a consequence, we derive the finiteness of the set of ergodic measures of maximal entropy, in the case where the entropy of the system is large. |
| title | Finitness of measured homoclinic classes with large Lyapunov exponents for $\mathcal{C}^2$ surface diffeomorphisms |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2504.19908 |