---
res:
  bibo_abstract:
  - 'Morse decompositions partition the flows in a vector field into equivalent structures.
    Given such a decomposition, one can define a further summary of its flow structure
    by what is called a connection matrix. These matrices, a generalization of Morse
    boundary operators from classical Morse theory, capture the connections made by
    the flows among the critical structures—such as attractors, repellers, and orbits—in
    a vector field. Recently, in the context of combinatorial dynamics, an efficient
    persistence-like algorithm to compute connection matrices has been proposed in
    Dey, Lipiński, Mrozek, and Slechta [SIAM J. Appl. Dyn. Syst., 23 (2024), pp. 81–97].
    We show that, actually, the classical persistence algorithm with exhaustive reduction
    retrieves connection matrices, both simplifying the algorithm of Dey et al. and
    bringing the theory of persistence closer to combinatorial dynamical systems.
    We supplement this main result with an observation: the concept of persistence
    as defined for scalar fields naturally adapts to Morse decompositions whose Morse
    sets are filtered with a Lyapunov function. We conclude by presenting preliminary
    experimental results.@eng'
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Tamal K.
      foaf_name: Dey, Tamal K.
      foaf_surname: Dey
  - foaf_Person:
      foaf_givenName: Andrew
      foaf_name: Haas, Andrew
      foaf_surname: Haas
  - foaf_Person:
      foaf_givenName: Michał
      foaf_name: Lipiński, Michał
      foaf_surname: Lipiński
      foaf_workInfoHomepage: http://www.librecat.org/personId=dfffb474-4317-11ee-8f5c-fe3fc95a425e
    orcid: 0000-0001-9789-9750
  bibo_doi: 10.1137/25m1739406
  bibo_issue: '1'
  bibo_volume: 25
  dct_date: 2026^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/1536-0040
  dct_language: eng
  dct_publisher: Society for Industrial & Applied Mathematics@
  dct_title: Computing a connection matrix and persistence efficiently from a morse
    decomposition@
...