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- W4301676225 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." @default.
- W4301676225 created "2022-10-05" @default.
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- W4301676225 date "2018-01-19" @default.
- W4301676225 modified "2023-09-27" @default.
- W4301676225 title "Persistent Homology of Morse Decompositions in Combinatorial Dynamics" @default.
- W4301676225 doi "https://doi.org/10.48550/arxiv.1801.06590" @default.
- W4301676225 hasPublicationYear "2018" @default.
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