Finding attracting sets using combinatorial multivector fields

82. Justin Thorpe, Thomas Wanner:
    Finding attracting sets using combinatorial multivector fields
    Preprint, submitted for publication, 6 pages, 2024.

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.

Bibtex

@article{thorpe:wanner:p24b,
   author = {Justin Thorpe and Thomas Wanner},
   title = {Finding attracting sets using combinatorial multivector fields},
   journal = {In preparation},
   year = 2024
   }