Categorical foundations of discrete dynamical systems
Dynamical Systems
2025-06-06 v1 Category Theory
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.
Cite
@article{arxiv.2506.05190,
title = {Categorical foundations of discrete dynamical systems},
author = {Daniel Carranza and Chris Kapulkin and Nathan Kershaw and Reinhard Laubenbacher and Matthew Wheeler},
journal= {arXiv preprint arXiv:2506.05190},
year = {2025}
}
Comments
30 pages; comments welcome