Expansive Minimal Flows
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909747343523840 |
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| author | Artigue, Alfonso Rego, Elias |
| author_facet | Artigue, Alfonso Rego, Elias |
| contents | In this paper, we extend a Mañé's famous result on expansive homeomorphisms, originally presented in [17], to the setting of flows. Specifically, we provide a complete characterization of minimal expansive flows without fixed points on compact metric spaces. We prove that such flows must be defined on one-dimensional sets and are equivalent to the suspension of a minimal subshift. This result significantly improves upon [16] by eliminating the need for their additional hypothesis. Furthermore, we apply our findings to show that any regular expansive flow on a compact metric space of dimension two or higher must contain infinitely many minimal subsets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10759 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Expansive Minimal Flows Artigue, Alfonso Rego, Elias Dynamical Systems Primary: 37B05, Secondary: 37B20 In this paper, we extend a Mañé's famous result on expansive homeomorphisms, originally presented in [17], to the setting of flows. Specifically, we provide a complete characterization of minimal expansive flows without fixed points on compact metric spaces. We prove that such flows must be defined on one-dimensional sets and are equivalent to the suspension of a minimal subshift. This result significantly improves upon [16] by eliminating the need for their additional hypothesis. Furthermore, we apply our findings to show that any regular expansive flow on a compact metric space of dimension two or higher must contain infinitely many minimal subsets. |
| title | Expansive Minimal Flows |
| topic | Dynamical Systems Primary: 37B05, Secondary: 37B20 |
| url | https://arxiv.org/abs/2502.10759 |