2018/09/05 by Andrei Alpeev, Alpeev, Andrei
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1809.01634
openalex publication_date 2018/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It was proved by Brudno that entropy and Kolmogorov complexity for dynamical systems are tightly related. We generalize his results to the case of arbitrary computable amenable group actions. Namely, for an ergodic shift-action, the asymptotic Kolmogorov complexity of a typical point is equal to the Kolmogorov-Sinai entropy of the action. For topological shift actions, the asymptotic Komogorov complexity of every point is bounded from above by the topological entropy, and there is a point attaining this bound.