Continuous maps of dendrites with finitely many branch points and nonwandering sets by Tatsuya Arai and Naotsugu Chinen

Topology Proceedings 26 No. 1 (2001-2002), pp. 29-36

Continuous maps of dendrites with finitely many branch points and nonwandering sets

Tatsuya Arai and Naotsugu Chinen

Let f be a continuous map of a dendrite X with finitely many branch points into itself and \Omega(f) the set of nonwandering points for f. We show the following two results: (1) if \Omega(f) is finite, it always is not the set of periodic points of f and (2) \Omega(f) is contained in the closure of the set of eventually periodic points of f.

Keywords: nonwandering set, dendrite, periodic point
Mathematics Subject Classification: 54H20 (54F50 54B20)

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Topology Proceedings, Volume 26 No. 1 (2001-2002)
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