Minimal flow morsification subject to level set control: a combinatorial approach
DOI:
https://doi.org/10.12775/TMNA.2024.049Keywords
Lyapunov graph, Morse-Conley theory, Poincaré-Hopf inequalities, network-flow theoryAbstract
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.References
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