Description

• Title:
  Minimal flow morsification subject to level set control: a combinatorial approach
• Creator:
  Bertolim, Maria Alice;
  de Rezende, Ketty Abaroa;
  Mello, Margarida Pinheiro
• Description:
  In this paper, we address both a combinatorial continuation question via Lyapunov graphs and the attainability of a preassigned level set, dubbed ground level set and given by its Betti numbers, within a morsification process of a dynamical configuration. The novelty introduced here is a componentwise Lyapunov graph morsification that keeps track of level sets during the morsification process subject to the minimality of the total number of singularities of a morsified flow. The algorithm behind the morsification translates into a system of linear equations whose feasibility is linked to that of a set of inequalities, called componentwise Poincaré-Hopf inequalities, involving the input data. This investigation combines techniques from both homological Conley index and network flow theories.
• Object availability:
  free access
• Date:
  2025.06.14
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Online First Articles; 1 - 55;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/62307/42815 ;https://apcz.umk.pl/TMNA/article/view/62307/42816
• Subject:
  Lyapunov graph;
  Morse-Conley theory;
  Poincaré-Hopf inequalities;
  network-flow theory;
  37B30, 37B35, 37B25
• Identifier: https://apcz.umk.pl/TMNA/article/view/62307
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other