Finding attracting sets using combinatorial multivector fields

79. Justin Thorpe, Thomas Wanner:
    Finding attracting sets using combinatorial multivector fields
    Accepted, but unpublished, manuscript, 6 pages, 2025.

Abstract

We discuss the identification of attracting sets using combinatorial multivector fields (CMVF) from Conley-Morse-Forman theory. A CMVF is a dynamical system induced by the action of a continuous dynamical system on a phase space discretization that can be represented as a Lefschetz complex. There is a rich theory under development establishing the connections between the induced and underlying dynamics and emphasizing computability. We introduce the main ideas behind this theory and demonstrate how it can be used to identify regions of interest within the global dynamics via graph-based algorithms and the connection matrix.

Note

This manuscript had been accepted for presentation and publication at the NOLCOS 25 conference. However, due to scheduling conflicts it was not possible for us to attend the conference, and therefore the paper did not get published. The preprint version of the paper can be downloaded from https://arxiv.org/abs/2503.23079.

Bibtex

@article{thorpe:wanner:25a,
   author = {Justin Thorpe and Thomas Wanner},
   title = {Finding attracting sets using combinatorial multivector fields},
   journal = {arXiv:2503.23079},
   note = {Accepted, but unpublished manuscript},
   year = 2025,
   doi = {10.48550/arXiv.2503.23079}
   }