Nonwandering points of monotone local dendrite maps revisited

摘要

Let X be a local dendrite and let f : X - X be a monotone map. Denote by P(f) and Omega(f) the sets of periodic points and nonwandering points of f, respectively. We show that Omega(f) = (P(f))over bar, whenever P(f) is nonempty and Omega(f) is the unique minimal set included in a circle which is either a Cantor set or a circle, whenever P(f) is empty. In the case where the set of endpoints of X is countable, we show that Omega(f) = P(f) whenever P(f) is nonempty. (C) 2018 Published by Elsevier B.V.