Resumen de Pointwise Recurrence on Local Dendrites

Ghassen Askri, Issam Naghmouchi

• In this paper, we prove that if X is a local dendrite different from the circle and f:X→X is a continuous map then f is pointwise recurrent if and only if it is a homeomorphism such that every cut point is periodic. Meanwhile, we show in the case of dendrites that the set of almost periodic points is a continuum and equals to the union of all ω-limit sets provided that the omega limit map is continuous and we show that it is only a necessary condition for the continuity of the omega limit map. We end the paper by suggesting some new open problems.