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There exist one-dimensional transitive cellular automata with non-empty set of strictly temporally periodic points

Matyja J.

Schedae Informaticae

2013

Vol. 22

41--45

In a Cantor metric space BZ; we present a one-sided cellular automaton which positively answers the question Does it exist a transitive cellular automaton (BZ; F) with non-empty set of strictly temporally periodic points? The question can be found in a current and recognized literature of the subject.

Strong transitivity and graph maps

Yokoi K.

Bulletin of the Polish Academy of Sciences. Mathematics

2005

Vol. 53, no 4

377-388

We study the relation between transitivity and strong transitivity, introduced by W. Parry, for graph self-maps. We establish that if a graph self-map f is transitive and the set of fixed points of fk is finite for each k ≥ 1, then f is strongly transitive. As a corollary, if a piecewise monotone graph self-map is transitive, then it is strongly transitive.