Continuity properties of partial entropy
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866909039947939840 |
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| author | Liao, Gang Tao, Huirong Tong, Yao Yang, Jiagang |
| author_facet | Liao, Gang Tao, Huirong Tong, Yao Yang, Jiagang |
| contents | We establish a general criterion on the upper semi-continuity of partial entropy in all directions for $C^{1+α}$ diffeomorphisms: it holds when the respective sums of Lyapunov exponents are continuous. This addresses, in arbitrary dimensions, the converse aspect of the entropic continuity of the Lyapunov exponents established by Buzzi, Crovisier, and Sarig. Consequently, the entropy (and all the partial entropies) is always upper semi-continuous at generic ergodic measures of every $C^{1+α}$ diffeomorphism, which extends the $C^{\infty}$ result of Newhouse.
Numerous applications and examples are provided, including topics related to measures with dominated splittings, SRB measures, average expanding diffeomorphisms, singular flows, standard maps, and symbolic codings for diffeomorphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_13273 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Continuity properties of partial entropy Liao, Gang Tao, Huirong Tong, Yao Yang, Jiagang Dynamical Systems We establish a general criterion on the upper semi-continuity of partial entropy in all directions for $C^{1+α}$ diffeomorphisms: it holds when the respective sums of Lyapunov exponents are continuous. This addresses, in arbitrary dimensions, the converse aspect of the entropic continuity of the Lyapunov exponents established by Buzzi, Crovisier, and Sarig. Consequently, the entropy (and all the partial entropies) is always upper semi-continuous at generic ergodic measures of every $C^{1+α}$ diffeomorphism, which extends the $C^{\infty}$ result of Newhouse. Numerous applications and examples are provided, including topics related to measures with dominated splittings, SRB measures, average expanding diffeomorphisms, singular flows, standard maps, and symbolic codings for diffeomorphisms. |
| title | Continuity properties of partial entropy |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2605.13273 |