Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.00136 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910039787175936 |
|---|---|
| author | Li, Kecheng |
| author_facet | Li, Kecheng |
| contents | We investigate the thermodynamic formalism for Viana maps-skew products obtained by coupling an expanding circle map with a slightly perturbed quadratic family on the fibers. For every Hölder potential $φ$ whose oscillation is below an explicit threshold, we show that an equilibrium state not only exists but is unique and satisfies an upper level-2 large-deviation principle. All of these conclusions persist under sufficiently small perturbations of the reference map. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_00136 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unique equilibrium states for Viana maps with small potentials Li, Kecheng Dynamical Systems We investigate the thermodynamic formalism for Viana maps-skew products obtained by coupling an expanding circle map with a slightly perturbed quadratic family on the fibers. For every Hölder potential $φ$ whose oscillation is below an explicit threshold, we show that an equilibrium state not only exists but is unique and satisfies an upper level-2 large-deviation principle. All of these conclusions persist under sufficiently small perturbations of the reference map. |
| title | Unique equilibrium states for Viana maps with small potentials |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2508.00136 |