Let X be a dendrite and f : X → X be a continuous map. Denote by R(f ) and P (f ) the sets of recurrent points and periodic points of f respectively. In this paper we show that, if the cardinal number Card(End(X)) of the set of endpoints of X is less than the cardinal number c of the continuum, then R = P . From this we derive that, if Card(End(X)) < c, then f is chaotic in the sense of Devaney if and only if f is transitive.
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