Relatively pointwise recurrence on local dendrites.

Let X be a local dendrite and let $ f:X\to X $ f : X → X be a continuous map. Denote by $ P(f) $ P (f) and $ R(f) $ R (f) the sets of periodic and recurrent points of f, respectively. We say that f is relatively pointwise recurrent if $ \overline {R(f)}=X $ R (f) ¯ = X. We show that, if X is almost meshed (i.e the union of the interior of all free arcs is dense in X), then f is relatively pointwise recurrent if and only if either f is topologically conjugate to an irrational rotation on the circle or it has a dense set of periodic points. [ABSTRACT FROM AUTHOR]