Weak Gibbs Measures for Local Homeomorphisms
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912668141486080 |
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| author | Ferreira, Giovane Ramos, Vanessa |
| author_facet | Ferreira, Giovane Ramos, Vanessa |
| contents | We study a broad class of local homeomorphisms and continuous potentials, proving the existence and uniqueness of weak Gibbs measures. From the Gibbs property, we show the uniqueness of equilibrium states and derive a large deviations principle. Furthermore, we extend these results to a class of attractors that are semiconjugate to local homeomorphisms from our original setting. Our approach is based on non-uniform conformal-like property and applies to a wide range of topological dynamical systems, including non-uniformly expanding maps, zooming local homeomorphisms, attractors arising from solenoid-like constructions and certain families of partially hyperbolic horseshoes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20938 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weak Gibbs Measures for Local Homeomorphisms Ferreira, Giovane Ramos, Vanessa Dynamical Systems 37A05, 37D35 We study a broad class of local homeomorphisms and continuous potentials, proving the existence and uniqueness of weak Gibbs measures. From the Gibbs property, we show the uniqueness of equilibrium states and derive a large deviations principle. Furthermore, we extend these results to a class of attractors that are semiconjugate to local homeomorphisms from our original setting. Our approach is based on non-uniform conformal-like property and applies to a wide range of topological dynamical systems, including non-uniformly expanding maps, zooming local homeomorphisms, attractors arising from solenoid-like constructions and certain families of partially hyperbolic horseshoes. |
| title | Weak Gibbs Measures for Local Homeomorphisms |
| topic | Dynamical Systems 37A05, 37D35 |
| url | https://arxiv.org/abs/2510.20938 |