Categorical foundations of discrete dynamical systems
arXiv:2506.05190
Abstract
We develop categorical foundations of discrete dynamical systems, aimed at understanding how the structure of the system affects its dynamics. We introduce the notion of cycle sets to analyze attractors of a system, and use this to generalize multiple decomposition theorems of Kadelka, Veliz-Cuba, Murrugarra, and the last two authors from Boolean networks to arbitrary discrete dynamical systems.
arXiv comment41 pages; comments still welcome