Categorical foundations of discrete dynamical systems

2025/06/05 by Carranza, Daniel, Kapulkin, Chris, Kershaw, Nathan +2
#18A99 #37N25 #92-10 #Category Theory (math.CT) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.05190

Abstract

We develop categorical foundations of discrete dynamical systems, aimed at understanding how the structure of the system affects its dynamics. The key technical innovation is the notion of a cycle set, which provides a formal language in which to speak of the system's attractors. As a proof of concept, we provide a decomposition theorem for discrete dynamical systems.

Citations

• Dynamical Systems and Sheaves

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