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math.DS2024
Cellular automata, percolation and dynamical dichotomies
Sebastián Barbieri, Felipe García-Ramos, Siamak Taati
We establish a connection between percolation on the Cayley graphs of a group and the dynamical diversity of cellular automata on that group. Specifically, we demonstrate that Gilm…
math.DS2024
Medvedev degrees of subshifts on groups
Sebastián Barbieri, Nicanor Carrasco-Vargas
The Medvedev degree of a subshift is a dynamical invariant of computable origin that can be used to compare the complexity of subshifts that contain only uncomputable configuration…
math.DS2024
Effective dynamical systems beyond dimension zero and factors of SFTs
Sebastián Barbieri, Nicanor Carrasco-Vargas, Cristóbal Rojas
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 represe…