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arXiv · 2506.05190

Categorical foundations of discrete dynamical systems

Daniel Carranza·Chris Kapulkin·Nathan Kershaw·Reinhard Laubenbacher·Matthew Wheeler
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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.

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Daniel Carranza, Chris Kapulkin, Nathan Kershaw, Reinhard Laubenbacher, Matthew Wheeler. 2026-08-29. Categorical foundations of discrete dynamical systems. https://arxiv.org/abs/2506.05190

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