Thermodynamic formalism for discontinuous maps and statistical properties of their equilibrium states
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908840019099648 |
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| author | Bilbao, Rafael Lucena, Rafael |
| author_facet | Bilbao, Rafael Lucena, Rafael |
| contents | In this article, we develop a functional-analytic framework to establish existence, uniqueness, regularity of disintegration, and statistical properties of equilibrium states for a broad class of dynamical systems, potentially discontinuous and not necessarily locally invertible. Our approach is applied to a family of piecewise partially hyperbolic maps and associated classes of potentials. We further prove several statistical limit theorems, including exponential decay of correlations, and propose related questions and conjectures. A collection of examples illustrating the applicability of our results is provided, including partially hyperbolic attractors over horseshoes, discontinuous systems, non-invertible dynamical systems admitting a semi-conjugacy to intermittent maps such as the Manneville--Pomeau map, and fat solenoidal attractors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_05577 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Thermodynamic formalism for discontinuous maps and statistical properties of their equilibrium states Bilbao, Rafael Lucena, Rafael Dynamical Systems 37A25, 37A10, 37C30, 37D50 In this article, we develop a functional-analytic framework to establish existence, uniqueness, regularity of disintegration, and statistical properties of equilibrium states for a broad class of dynamical systems, potentially discontinuous and not necessarily locally invertible. Our approach is applied to a family of piecewise partially hyperbolic maps and associated classes of potentials. We further prove several statistical limit theorems, including exponential decay of correlations, and propose related questions and conjectures. A collection of examples illustrating the applicability of our results is provided, including partially hyperbolic attractors over horseshoes, discontinuous systems, non-invertible dynamical systems admitting a semi-conjugacy to intermittent maps such as the Manneville--Pomeau map, and fat solenoidal attractors. |
| title | Thermodynamic formalism for discontinuous maps and statistical properties of their equilibrium states |
| topic | Dynamical Systems 37A25, 37A10, 37C30, 37D50 |
| url | https://arxiv.org/abs/2311.05577 |