On One-Sided, Topologically Mixing and Strongly Transitive CA with a Continuum of Period-Two Points
Wit Foryś and Janusz Matyja
In a metric Cantor space BNn (BZn) for any integer n ≥ 2 we present a modified construction of a one-sided, topologically mixing, open and strongly transitive cellular automaton (BNn (BZn) , Fn ) with radius r = 1. The automaton has no fixed points but has continuum of period-two points and topological entropy log(n). Additionally, in restriction to BNn, it has a dense set of strictly temporally periodic points. The construction guarantees the strong transitivity of (BZn , Fn ), and it is based on the cellular automaton (BN, F) with radius r = 1, defined for any prime number p. We have proved in our previous paper that (BN, F) is non-injective, chaotic in Devaney sense, has no fixed points but has continuum of period-two points and topological entropy log(p). In this paper we prove that it has the remaining mentioned properties of (BNn , Fn).
Keywords: One-sided cellular automata, topologically mixing, strongly transitive, left-permutative, right-closing, strictly temporally periodic points, topological entropy.