Nonwandering sets and special $α$-limit sets of monotone maps on regular curves

Abstract

Let X be a regular curve and let f : X → X be a monotone map. In this paper, nonwandering set of f and the structure of special α-limit sets for f are investigated. We show that AP(f ) = R(f ) = Ω(f ), where AP(f ), R(f ) and Ω(f ) are the sets of almost periodic points, recurrent points and nonwandering of f , respectively. This result extends that of Naghmouchi established, whenever f is a homeomorphism on a regular curve [