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arXiv · 1801.06590

Persistent Homology of Morse Decompositions in Combinatorial Dynamics

Tamal K. Dey·Mateusz Juda·Tomasz Kapela·Jacek Kubica·Michal Lipinski·Marian Mrozek
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Abstract

We investigate combinatorial dynamical systems on simplicial complexes considered as {\em finite topological spaces}. Such systems arise in a natural way from sampling dynamics and may be used to reconstruct some features of the dynamics directly from the sample. We study the homological persistence of {\em Morse decompositions} of such systems, an important descriptor of the dynamics, as a tool for validating the reconstruction. Our framework can be viewed as a step toward extending the classical persistence theory to "vector cloud" data. We present experimental results on two numerical examples.

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Tamal K. Dey, Mateusz Juda, Tomasz Kapela, Jacek Kubica, Michal Lipinski, Marian Mrozek. 2018-01-19. Persistent Homology of Morse Decompositions in Combinatorial Dynamics. https://arxiv.org/abs/1801.06590

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