License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2022.35
URN: urn:nbn:de:0030-drops-160439
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16043/
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Dey, Tamal K. ; Lipiński, Michał ; Mrozek, Marian ; Slechta, Ryan

Tracking Dynamical Features via Continuation and Persistence

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Abstract

Multivector fields and combinatorial dynamical systems have recently become a subject of interest due to their potential for use in computational methods. In this paper, we develop a method to track an isolated invariant set - a salient feature of a combinatorial dynamical system - across a sequence of multivector fields. This goal is attained by placing the classical notion of the "continuation" of an isolated invariant set in the combinatorial setting. In particular, we give a "Tracking Protocol" that, when given a seed isolated invariant set, finds a canonical continuation of the seed across a sequence of multivector fields. In cases where it is not possible to continue, we show how to use zigzag persistence to track homological features associated with the isolated invariant sets. This construction permits viewing continuation as a special case of persistence.

BibTeX - Entry

@InProceedings{dey_et_al:LIPIcs.SoCG.2022.35,
  author =	{Dey, Tamal K. and Lipi\'{n}ski, Micha{\l} and Mrozek, Marian and Slechta, Ryan},
  title =	{{Tracking Dynamical Features via Continuation and Persistence}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{35:1--35:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16043},
  URN =		{urn:nbn:de:0030-drops-160439},
  doi =		{10.4230/LIPIcs.SoCG.2022.35},
  annote =	{Keywords: combinatorial dynamical systems, continuation, index pair, Conley index, persistent homology}
}

Keywords: combinatorial dynamical systems, continuation, index pair, Conley index, persistent homology
Collection: 38th International Symposium on Computational Geometry (SoCG 2022)
Issue Date: 2022
Date of publication: 01.06.2022

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