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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/2510.18804 |
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| _version_ | 1866915567902916608 |
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| author | Delplanque, Alexandre Li, Hengyi |
| author_facet | Delplanque, Alexandre Li, Hengyi |
| contents | We prove the entropic continuity of Lyapunov exponent for C^r maps of the interval or of the circle with large entropy for r>1, without making any assumptions on the set of critical points. A consequence is the upper semi-continuity of entropy at ergodic measures with large entropy. Another consequence is the uniform integrability of the geometric potential at ergodic measures with large entropy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_18804 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Continuity of Lyapunov exponents for C^r one-dimensional maps Delplanque, Alexandre Li, Hengyi Dynamical Systems We prove the entropic continuity of Lyapunov exponent for C^r maps of the interval or of the circle with large entropy for r>1, without making any assumptions on the set of critical points. A consequence is the upper semi-continuity of entropy at ergodic measures with large entropy. Another consequence is the uniform integrability of the geometric potential at ergodic measures with large entropy. |
| title | Continuity of Lyapunov exponents for C^r one-dimensional maps |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2510.18804 |