2024/01/15 by Sebastián Barbieri, Barbieri, Sebastián, Nicanor Carrasco-Vargas +3 · 1 citation
Computer Science · Mathematics · #03D78 #20F10 #37B02 #37B10 #Cellular Automata and Applications #Computability, Logic, AI Algorithms #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2401.07973
openalex publication_date 2024/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using tools from computable analysis we develop a notion of effectiveness for general dynamical systems as those group actions on arbitrary spaces that contain a computable representative in their topological conjugacy class. Most natural systems one can think of are effective in this sense, including some group rotations, affine actions on the torus and finitely presented algebraic actions. We show that for finitely generated and recursively presented groups, every effective dynamical system is the topological factor of a computable action on an effectively closed subset of the Cantor space. We then apply this result to extend the simulation results available in the literature beyond zero-dimensional spaces. In particular, we show that for a large class of groups, many of these natural actions are topological factors of subshifts of finite type.