Topological and metric emergence of continuous maps
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
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| _version_ | 1866915093031157760 |
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| author | Carvalho, Maria Rodrigues, Fagner B. Varandas, Paulo |
| author_facet | Carvalho, Maria Rodrigues, Fagner B. Varandas, Paulo |
| contents | We prove that the homeomorphisms of a compact manifold with dimension one have zero topological emergence, whereas in dimension greater than one the topological emergence of a C^0-generic conservative homeomorphism is maximal, equal to the dimension of the manifold. Moreover, we show that the metric emergence of continuous self-maps on compact metric spaces has the intermediate value property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_00962 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Topological and metric emergence of continuous maps Carvalho, Maria Rodrigues, Fagner B. Varandas, Paulo Dynamical Systems 37C45, 54H20, 37B40, 54F45 We prove that the homeomorphisms of a compact manifold with dimension one have zero topological emergence, whereas in dimension greater than one the topological emergence of a C^0-generic conservative homeomorphism is maximal, equal to the dimension of the manifold. Moreover, we show that the metric emergence of continuous self-maps on compact metric spaces has the intermediate value property. |
| title | Topological and metric emergence of continuous maps |
| topic | Dynamical Systems 37C45, 54H20, 37B40, 54F45 |
| url | https://arxiv.org/abs/2208.00962 |