Persistent Homology of Morse Decompositions in Combinatorial Dynamics
Algebraic Topology
2018-07-12 v2 Computational Geometry
Dynamical Systems
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.
Keywords
Cite
@article{arxiv.1801.06590,
title = {Persistent Homology of Morse Decompositions in Combinatorial Dynamics},
author = {Tamal K. Dey and Mateusz Juda and Tomasz Kapela and Jacek Kubica and Michal Lipinski and Marian Mrozek},
journal= {arXiv preprint arXiv:1801.06590},
year = {2018}
}