Conley index for multivalued maps on finite topological spaces

83. Jonathan Barmak, Marian Mrozek, Thomas Wanner:
    Conley index for multivalued maps on finite topological spaces
    Foundations of Computational Mathematics 26(2), pp. 647-687, 2026.

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.

Links

The preprint version of the paper can be downloaded from https://arxiv.org/abs/2310.03099, while the published version of the paper can be found at https://doi.org/10.1007/s10208-024-09685-4.

Bibtex

@article{barmak:etal:26a,
   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 = 2026,
   volume = {26},
   number = {2},
   pages = {647--687},
   doi = {10.1007/s10208-024-09685-4}
   }