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arXiv · 2310.03099

Conley index for multivalued maps on finite topological spaces

Jonathan Barmak·Marian Mrozek·Thomas Wanner
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Abstract

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.

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Jonathan Barmak, Marian Mrozek, Thomas Wanner. 2023-10-04. Conley index for multivalued maps on finite topological spaces. https://arxiv.org/abs/2310.03099

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