Entropy structures with continuous partitions of unity
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910089808445440 |
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| author | Carrand, Jérôme |
| author_facet | Carrand, Jérôme |
| contents | Using only continuous partitions of unity, we provide equivalent definitions for the metric, topological and topological tail entropies and pressures of a continuous self-map of a compact set, as well as their conditional versions. A tail variational principle for these new definitions is proved. We extend Downarowicz's notions of candidates and entropy structures to account for almost-increasing sequences of functions arising from the new definitions. Finally, we deduce a partial answer to a question raised by Newhouse. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29720 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Entropy structures with continuous partitions of unity Carrand, Jérôme Dynamical Systems 37A35 37B40 37D35 Using only continuous partitions of unity, we provide equivalent definitions for the metric, topological and topological tail entropies and pressures of a continuous self-map of a compact set, as well as their conditional versions. A tail variational principle for these new definitions is proved. We extend Downarowicz's notions of candidates and entropy structures to account for almost-increasing sequences of functions arising from the new definitions. Finally, we deduce a partial answer to a question raised by Newhouse. |
| title | Entropy structures with continuous partitions of unity |
| topic | Dynamical Systems 37A35 37B40 37D35 |
| url | https://arxiv.org/abs/2603.29720 |