A large class of dendrite maps for which M\"{o}bius disjointness property of Sarnak is fulfilled

Abstract

We prove that any dendrite map for which the set of endpoints is closed and countable fulfilled Sarnak M\"{o}bius disjointness. This extended a result by el Abdalaoui-Askri and Marzougui \cite{ela-GH}. We further notice that the Smital-Ruelle property can be extended to the class of dendrites with closed and countable endpoints.