Möbius disjointness conjecture for local dendrite maps

Abstract

We prove that the Möbius disjointness conjecture holds for graph maps with zero topological entropy and for all monotone local dendrite maps. We further show that this also holds for continuous maps on certain class of dendrites. Moreover, we see that there is an example of transitive dendrite map with zero entropy for which Möbius disjointness conjecture holds.