Ergodicity, transitivity, and regularity for linear cellular automata over Z(m)
We study the dynamical behavior of D-dimensional linear cellular automata over Z(m). We provide an easy-to-check necessary and sufficient condition for a D-dimensional linear cellular automata over Z(m) to be ergodic and topologically transitive. As a byproduct, we get that for linear cellular automata ergodicity is equivalent to topological transitivity. Finally, we prove that for 1-dimensional linear cellular automata over Z(m), regularity (denseness of periodic orbits) is equivalent to surjectivity. (C) 2000 Elsevier Science B.V. All rights reserved.
ergodicity cellular automata topological transitivity discrete time dynamical systems