Abstract
Let X be a local dendrite and let f:X→X be a monotone map. Denote by P(f) and Ω(f) the sets of periodic points and nonwandering points of f, respectively. We show that Ω(f)=P(f)‾, whenever P(f) is nonempty and Ω(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 Ω(f)=P(f) whenever P(f) is nonempty.
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