Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2304.05996 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912872252047360 |
|---|---|
| author | Bhullar, Jasmine |
| author_facet | Bhullar, Jasmine |
| contents | For full shifts on finite alphabets, Coelho and Quas showed that the map that sends a Hölder continuous potential $ϕ$ to its equilibrium state $μ_ϕ$ is $\overline{d}$-continuous. We extend this result to the setting of full shifts on countable (infinite) alphabets. As part of the proof, we show that the map that sends a strongly positive recurrent potential to its normalization is continuous for potentials on mixing countable state Markov shifts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_05996 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $\overline{d}$-continuity for countable state shifts Bhullar, Jasmine Dynamical Systems For full shifts on finite alphabets, Coelho and Quas showed that the map that sends a Hölder continuous potential $ϕ$ to its equilibrium state $μ_ϕ$ is $\overline{d}$-continuous. We extend this result to the setting of full shifts on countable (infinite) alphabets. As part of the proof, we show that the map that sends a strongly positive recurrent potential to its normalization is continuous for potentials on mixing countable state Markov shifts. |
| title | $\overline{d}$-continuity for countable state shifts |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2304.05996 |