Nonwandering sets and the entropy of local homeomorphisms
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914969503662080 |
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| author | Gonçalves, Daniel Royer, Danilo Tasca, Felipe Augusto |
| author_facet | Gonçalves, Daniel Royer, Danilo Tasca, Felipe Augusto |
| contents | A local homeomorphism between open subsets of a locally compact Hausdorff space induces dynamical systems with a wide range of applications, including in C*-algebras. In this paper, we introduce the concepts of nonwandering and wandering sets for such systems and show that, under mild conditions, the metric entropy is concentrated in the nonwandering set. More generally, we demonstrate that the entropy of the system is the maximum of the entropies of the systems restricted to the nonwandering set and the closure of the wandering set. We illustrate these results with several examples, including applications to subshifts over countable alphabets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08072 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonwandering sets and the entropy of local homeomorphisms Gonçalves, Daniel Royer, Danilo Tasca, Felipe Augusto Dynamical Systems Operator Algebras Primary: 37B40, Secondary: 37B10, 37A35, 37A55, 54C70, A local homeomorphism between open subsets of a locally compact Hausdorff space induces dynamical systems with a wide range of applications, including in C*-algebras. In this paper, we introduce the concepts of nonwandering and wandering sets for such systems and show that, under mild conditions, the metric entropy is concentrated in the nonwandering set. More generally, we demonstrate that the entropy of the system is the maximum of the entropies of the systems restricted to the nonwandering set and the closure of the wandering set. We illustrate these results with several examples, including applications to subshifts over countable alphabets. |
| title | Nonwandering sets and the entropy of local homeomorphisms |
| topic | Dynamical Systems Operator Algebras Primary: 37B40, Secondary: 37B10, 37A35, 37A55, 54C70, |
| url | https://arxiv.org/abs/2410.08072 |