Linking combinatorial and classical dynamics: Conley index and Morse decompositions
Dynamical Systems
2020-05-29 v1
Abstract
We prove that every combinatorial dynamical system in the sense of Forman, defined on a family of simplices of a simplicial complex, gives rise to a multivalued dynamical system F on the geometric realization of the simplicial complex. Moreover, F may be chosen in such a way that the isolated invariant sets, Conley indices, Morse decompositions, and Conley-Morse graphs of the two dynamical systems are in one-to-one correspondence.
Cite
@article{arxiv.1710.05802,
title = {Linking combinatorial and classical dynamics: Conley index and Morse decompositions},
author = {Bogdan Batko and Tomasz Kaczynski and Marian Mrozek and Thomas Wanner},
journal= {arXiv preprint arXiv:1710.05802},
year = {2020}
}