On some aspects of local thermodynamical formalism
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866918263630331904 |
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| author | Bis, Andrzej Bruin, Henk |
| author_facet | Bis, Andrzej Bruin, Henk |
| contents | In 2007, Ye \& Zhang introduced a version of local topological entropy. Since their entropy function is, as we show under mild conditions, constant for topologically transitive dynamical systems, we propose to adjust the notion in a way that does not neglect the initial transient part of an orbit. We investigate the properties of this ``transient'' version, which we call translocal entropy, and compute it in terms of Lyapunov exponents for various dynamical systems. We also investigate how this adjustment affects measure-theoretic local (Brin-Katok) entropy and local pressure functions, generalizing some partial variation principles of Ma \& Wen. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_04055 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On some aspects of local thermodynamical formalism Bis, Andrzej Bruin, Henk Dynamical Systems 37B40, 37A35 In 2007, Ye \& Zhang introduced a version of local topological entropy. Since their entropy function is, as we show under mild conditions, constant for topologically transitive dynamical systems, we propose to adjust the notion in a way that does not neglect the initial transient part of an orbit. We investigate the properties of this ``transient'' version, which we call translocal entropy, and compute it in terms of Lyapunov exponents for various dynamical systems. We also investigate how this adjustment affects measure-theoretic local (Brin-Katok) entropy and local pressure functions, generalizing some partial variation principles of Ma \& Wen. |
| title | On some aspects of local thermodynamical formalism |
| topic | Dynamical Systems 37B40, 37A35 |
| url | https://arxiv.org/abs/2412.04055 |