On the loss of upper semi-continuity of metric entropy for $C^{r}$ diffeomorphisms
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913009968873472 |
|---|---|
| author | Bai, Xinyu Lin, Wanshan Tian, Xueting |
| author_facet | Bai, Xinyu Lin, Wanshan Tian, Xueting |
| contents | In this article, we give an upper bound estimate for the quantitative loss of the upper semi-continuity of the metric entropy for $C^r\:(r>1)$ diffeomorphisms. Building on earlier entropy estimates and reparametrization methods, we optimize the upper bound estimate with respect to both dimension and asymptotic Lipschitz constant. Motivated by Buzzi's examples, we show that the estimate is sharp. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05611 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the loss of upper semi-continuity of metric entropy for $C^{r}$ diffeomorphisms Bai, Xinyu Lin, Wanshan Tian, Xueting Dynamical Systems In this article, we give an upper bound estimate for the quantitative loss of the upper semi-continuity of the metric entropy for $C^r\:(r>1)$ diffeomorphisms. Building on earlier entropy estimates and reparametrization methods, we optimize the upper bound estimate with respect to both dimension and asymptotic Lipschitz constant. Motivated by Buzzi's examples, we show that the estimate is sharp. |
| title | On the loss of upper semi-continuity of metric entropy for $C^{r}$ diffeomorphisms |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2604.05611 |