Upper semi-continuity of metric entropy for $\mathcal{C}^{1,α}$ diffeomorphisms
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916687395160064 |
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| author | Luo, Chiyi Yang, Dawei |
| author_facet | Luo, Chiyi Yang, Dawei |
| contents | We prove that for $\mathcal{C}^{1,α}$ diffeomorphisms on a compact manifold $M$ with ${\rm dim} M\leq 3$, if an invariant measure $μ$ is a continuity point of the sum of positive Lyapunov exponents, then $μ$ is an upper semi-continuity point of the entropy map. This gives several consequences, such as the upper-semi continuity of dimensions of measures for surface diffeomorphisms. Furthermore, we know the continuity of dimensions for measures of maximal entropy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07746 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Upper semi-continuity of metric entropy for $\mathcal{C}^{1,α}$ diffeomorphisms Luo, Chiyi Yang, Dawei Dynamical Systems We prove that for $\mathcal{C}^{1,α}$ diffeomorphisms on a compact manifold $M$ with ${\rm dim} M\leq 3$, if an invariant measure $μ$ is a continuity point of the sum of positive Lyapunov exponents, then $μ$ is an upper semi-continuity point of the entropy map. This gives several consequences, such as the upper-semi continuity of dimensions of measures for surface diffeomorphisms. Furthermore, we know the continuity of dimensions for measures of maximal entropy. |
| title | Upper semi-continuity of metric entropy for $\mathcal{C}^{1,α}$ diffeomorphisms |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2504.07746 |