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Categorical foundations of discrete dynamical systems
Published 5 Jun 2025 in math.DS and math.CT | (2506.05190v1)
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.
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