Recurrence and nonwandering sets of local dendrite maps

Abstract

Given a local dendrite X with set End(X) of endpoints of X countable and be a continuous map, we let , , , , , the sets of periodic points, almost periodic points, recurrent points, nonwandering points, eventually periodic points and eventually almost periodic points of f, respectively. We show that . On the other hand, we show that , whenever . As a consequence, we prove that if the set of branch points is finite, then . We give a counter-example showing that the above results do not hold whenever is infinite or End(X) is uncountable.