Strong Transitivity and Graph Maps

Volume 53 / 2005

Katsuya Yokoi 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.

Authors

  • Katsuya YokoiDepartment of Mathematics
    Shimane University
    Matsue, 690-8504, Japan
    e-mail

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