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

AbstractWe study the dynamical behavior of D-dimensional linear cellular automata over Zm. We provide easy-to-check necessary and sufficient conditions for a D-dimensional linear cellular automata over Zm 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 Zm according to the most important dynamical properties studied in the theory of discrete time dynamical systems