Conley index for multivalued maps on finite topological spaces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909179524939776 |
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| author | Barmak, Jonathan Mrozek, Marian Wanner, Thomas |
| author_facet | Barmak, Jonathan Mrozek, Marian Wanner, Thomas |
| contents | We develop Conley's theory for multivalued maps on finite topological spaces. More precisely, for discrete-time dynamical systems generated by the iteration of a multivalued map which satisfies appropriate regularity conditions, we establish the notions of isolated invariant sets and index pairs, and use them to introduce a well-defined Conley index. In addition, we verify some of its fundamental properties such as the Wazewski property and continuation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_03099 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Conley index for multivalued maps on finite topological spaces Barmak, Jonathan Mrozek, Marian Wanner, Thomas Dynamical Systems Algebraic Topology Primary: 37B30, Secondary: 37E15, 57M99, 57Q05, 57Q15 We develop Conley's theory for multivalued maps on finite topological spaces. More precisely, for discrete-time dynamical systems generated by the iteration of a multivalued map which satisfies appropriate regularity conditions, we establish the notions of isolated invariant sets and index pairs, and use them to introduce a well-defined Conley index. In addition, we verify some of its fundamental properties such as the Wazewski property and continuation. |
| title | Conley index for multivalued maps on finite topological spaces |
| topic | Dynamical Systems Algebraic Topology Primary: 37B30, Secondary: 37E15, 57M99, 57Q05, 57Q15 |
| url | https://arxiv.org/abs/2310.03099 |