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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.