A variational principle for metric mean dimension via lower Brin-Katok local entropy
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916066347712512 |
|---|---|
| author | Shi, Ruxi |
| author_facet | Shi, Ruxi |
| contents | We prove a finite-scale comparison between lower Brin-Katok local entropy and Katok covering entropy. Let $(\mathcal{X},d,T)$ be a compact metric topological dynamical system and let $μ$ be ergodic. Then, for every $ε>0$ and every $δ\in(0,1)$, $$
h^K_μ(6ε,δ)\leq \underline h^{BK}_μ(ε). $$ Combining this estimate with the usual Katok-type variational principle for metric mean dimension gives the corresponding variational principle with lower Brin-Katok local entropy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_31407 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A variational principle for metric mean dimension via lower Brin-Katok local entropy Shi, Ruxi Dynamical Systems We prove a finite-scale comparison between lower Brin-Katok local entropy and Katok covering entropy. Let $(\mathcal{X},d,T)$ be a compact metric topological dynamical system and let $μ$ be ergodic. Then, for every $ε>0$ and every $δ\in(0,1)$, $$ h^K_μ(6ε,δ)\leq \underline h^{BK}_μ(ε). $$ Combining this estimate with the usual Katok-type variational principle for metric mean dimension gives the corresponding variational principle with lower Brin-Katok local entropy. |
| title | A variational principle for metric mean dimension via lower Brin-Katok local entropy |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2605.31407 |