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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2309.11410 |
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| _version_ | 1866911884190416896 |
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| author | Climenhaga, Vaughn Day, Jason |
| author_facet | Climenhaga, Vaughn Day, Jason |
| contents | Given a two-sided shift space on a finite alphabet and a continuous potential function, we give conditions under which an equilibrium measure can be described using a construction analogous to Hausdorff measure that goes back to the work of Bowen. This construction was previously applied to smooth uniformly and partially hyperbolic systems by the first author, Pesin, and Zelerowicz. Our results here apply to all subshifts of finite type and Hölder continuous potentials, but extend beyond this setting, and we also apply them to shift spaces with synchronizing words. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_11410 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Equilibrium measures for two-sided shift spaces via dimension theory Climenhaga, Vaughn Day, Jason Dynamical Systems Given a two-sided shift space on a finite alphabet and a continuous potential function, we give conditions under which an equilibrium measure can be described using a construction analogous to Hausdorff measure that goes back to the work of Bowen. This construction was previously applied to smooth uniformly and partially hyperbolic systems by the first author, Pesin, and Zelerowicz. Our results here apply to all subshifts of finite type and Hölder continuous potentials, but extend beyond this setting, and we also apply them to shift spaces with synchronizing words. |
| title | Equilibrium measures for two-sided shift spaces via dimension theory |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2309.11410 |