Thomas Wanner
Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, Virginia 22030, USA

 

Conley index for multivalued maps on finite topological spaces

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  1. Jonathan Barmak, Marian Mrozek, Thomas Wanner:
    Conley index for multivalued maps on finite topological spaces
    Foundations of Computational Mathematics, accepted for publication, 43 pages, 2024.

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.

The preprint version of the paper can be downloaded from https://arxiv.org/abs/2310.03099.

Bibtex

@article{barmak:etal:p24a,
   author = {Jonathan Barmak and Marian Mrozek and Thomas Wanner},
   title = {Conley index for multivalued maps on finite topological spaces},
   journal = {Foundations of Computational Mathematics},
   year = 2024,
   pages = {43~pages},
   note = {accepted for publication}
   }