Pointwise-recurrent dendrite maps
Dynamical Systems
2011-08-16 v1
Abstract
Let D be a dendrite and f:D-> D a continuous map. Denote by E(D) and B(D) the sets of endpoints and branch points of D respectively. We show that if E(D) is countable (resp. B(D) is discrete) then f is pointwise-recurrent if and only if f is pointwise periodic homeomorphism (resp. every pointin D\E(D) is periodic).
Cite
@article{arxiv.1108.2787,
title = {Pointwise-recurrent dendrite maps},
author = {Issam Naghmouchi},
journal= {arXiv preprint arXiv:1108.2787},
year = {2011}
}