Mappings on dendrites

The existence of a point of order ω in dendrites with finitely many branch points is characterized in terms of self-mappings on such dendrites. Also in these terms conditions are found under which dendrites without points of order ω have infinitely many branch points. Structure of dendrites having the ΩEP-property (for each self-mapping f the set of nonwandering points of f is contained in the closure of the set of eventually periodic points of f) is characterized by noncontaining of a special dendrite W.