Linking combinatorial and classical dynamics: Conley index and Morse decompositions

69. Bogdan Batko, Tomasz Kaczynski, Marian Mrozek, Thomas Wanner:
    Linking combinatorial and classical dynamics: Conley index and Morse decompositions
    Foundations of Computational Mathematics 20(5), pp. 967-1012, 2020.

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 combinatorial vector field give rise to isomorphic objects in the multivalued map case.

Links

The preprint version of the paper can be downloaded from https://arxiv.org/abs/1710.05802, while the published version of the paper can be found at https://doi.org/10.1007/s10208-020-09444-1.

Bibtex

@article{batko:etal:20a,
   author = {Bogdan Batko and Tomasz Kaczynski and Marian Mrozek and Thomas Wanner},
   title = {Linking combinatorial and classical dynamics: {C}onley
            index and {M}orse decompositions},
   journal = {Foundations of Computational Mathematics},
   volume = {20},
   number = {5},
   year = {2020},
   pages = {967--1012},
   doi = {10.1007/s10208-020-09444-1}
   }