Strong Transitivity and Graph Maps
Volume 53 / 2005
Bulletin Polish Acad. Sci. Math. 53 (2005), 377-388
MSC: 37E25, 37B20.
DOI: 10.4064/ba53-4-3
Abstract
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 $f^{k}$ is finite for each $k \geq 1$, then $f$ is strongly transitive. As a corollary, if a piecewise monotone graph self-map is transitive, then it is strongly transitive.
