Thermodynamic formalism for random non-uniformly expanding maps
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2020
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| Acceso en línea: | |
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| _version_ | 1866911844219748352 |
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| author | Stadlbauer, Manuel Suzuki, Shintaro Varandas, Paulo |
| author_facet | Stadlbauer, Manuel Suzuki, Shintaro Varandas, Paulo |
| contents | We develop a quenched thermodynamic formalism for a wide class of random maps with non-uniform expansion, where no Markov structure, no uniformly bounded degree or the existence of some expanding dynamics is required. We prove that every measurable and fibered $C^1$-potential at high temperature admits a unique equilibrium state which satisfies a weak Gibbs property, and has exponential decay of correlations. The arguments combine a functional analytic approach for the decay of correlations (using Birkhoff cone methods) and Carathéodory-type structures to describe the relative pressure of not necessary compact invariant sets in random dynamical systems. We establish also a variational principle for the relative pressure of random dynamical systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_03749 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Thermodynamic formalism for random non-uniformly expanding maps Stadlbauer, Manuel Suzuki, Shintaro Varandas, Paulo Dynamical Systems We develop a quenched thermodynamic formalism for a wide class of random maps with non-uniform expansion, where no Markov structure, no uniformly bounded degree or the existence of some expanding dynamics is required. We prove that every measurable and fibered $C^1$-potential at high temperature admits a unique equilibrium state which satisfies a weak Gibbs property, and has exponential decay of correlations. The arguments combine a functional analytic approach for the decay of correlations (using Birkhoff cone methods) and Carathéodory-type structures to describe the relative pressure of not necessary compact invariant sets in random dynamical systems. We establish also a variational principle for the relative pressure of random dynamical systems. |
| title | Thermodynamic formalism for random non-uniformly expanding maps |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2006.03749 |