Nonadditive families of potentials: physical equivalence and some regularity relations
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866914214978781184 |
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| author | Holanda, Carllos Eduardo |
| author_facet | Holanda, Carllos Eduardo |
| contents | We show that additive and asymptotically additive families of continuous functions with respect to suspension flows are physically equivalent. In particular, the equivalence result holds for hyperbolic flows and some classes of expansive flows in general. Moreover, we show how this equivalence result can be used to extend the nonadditive thermodynamic formalism and multifractal analysis. In the second part of this work, we obtain a Livšic-like result for nonadditive families of potentials and also address the Hölder and Bowen regularity problem for the physical equivalence relations with respect to hyperbolic symbolic flows. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_05926 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Nonadditive families of potentials: physical equivalence and some regularity relations Holanda, Carllos Eduardo Dynamical Systems 28D10, 37D35 We show that additive and asymptotically additive families of continuous functions with respect to suspension flows are physically equivalent. In particular, the equivalence result holds for hyperbolic flows and some classes of expansive flows in general. Moreover, we show how this equivalence result can be used to extend the nonadditive thermodynamic formalism and multifractal analysis. In the second part of this work, we obtain a Livšic-like result for nonadditive families of potentials and also address the Hölder and Bowen regularity problem for the physical equivalence relations with respect to hyperbolic symbolic flows. |
| title | Nonadditive families of potentials: physical equivalence and some regularity relations |
| topic | Dynamical Systems 28D10, 37D35 |
| url | https://arxiv.org/abs/2210.05926 |