2026-07-22T10:50:41Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:12195 2024-03-06T10:49:40Z ddc:004 open_access

Persistence of the Conley Index in Combinatorial Dynamical Systems Dey, Tamal K. Mrozek, Marian Slechta, Ryan Dynamical systems combinatorial vector field multivector Conley index persistence A combinatorial framework for dynamical systems provides an avenue for connecting classical dynamics with data-oriented, algorithmic methods. Combinatorial vector fields introduced by Forman [R. Forman, 1998; R. Forman, 1998] and their recent generalization to multivector fields [Mrozek, 2017] have provided a starting point for building such a connection. In this work, we strengthen this relationship by placing the Conley index in the persistent homology setting. Conley indices are homological features associated with so-called isolated invariant sets, so a change in the Conley index is a response to perturbation in an underlying multivector field. We show how one can use zigzag persistence to summarize changes to the Conley index, and we develop techniques to capture such changes in the presence of noise. We conclude by developing an algorithm to "track" features in a changing multivector field. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Tamal K. Dey and Marian Mrozek and Ryan Slechta 2020 Is Part Of LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2020.37 urn:nbn:de:0030-drops-121958 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.37 eng https://creativecommons.org/licenses/by/3.0/legalcode