Conley index for multivalued maps on finite topological spaces
Dynamical Systems
2024-04-25 v2 Algebraic Topology
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.
Keywords
Cite
@article{arxiv.2310.03099,
title = {Conley index for multivalued maps on finite topological spaces},
author = {Jonathan Barmak and Marian Mrozek and Thomas Wanner},
journal= {arXiv preprint arXiv:2310.03099},
year = {2024}
}