A complete and efficiently computable topological classification of D-dimensional linear cellular automata over Z_m

摘要

We study the dynamical behavior of D-dimensional linear cellular automata over Z_m. We provide easy-to-check necessary and sufficient conditions for a D-dimensional linear cellular automata over Z_m to be sensitive to initial conditions, positively expansive, strongly transitive, and equicontinuous. As a consequence of our results, we have a complete and efficiently computable topological classification of D-dimensional linear cellular automata over Z_m according to the most important dynamical properties studied in the theory of discrete time dynamical systems.