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arXiv · 1710.05802

Linking combinatorial and classical dynamics: Conley index and Morse decompositions

Bogdan Batko·Tomasz Kaczynski·Marian Mrozek·Thomas Wanner
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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.

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Bogdan Batko, Tomasz Kaczynski, Marian Mrozek, Thomas Wanner. 2017-10-16. Linking combinatorial and classical dynamics: Conley index and Morse decompositions. https://doi.org/10.1007/s10208-020-09444-1

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