Conley index for multivalued maps on finite topological spaces

Jonathan Barmak, Marian Mrozek, Thomas Wanner

Published 2023-10-04Version 1

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.