Mobius disjointness conjecture for local dendrite maps

Abstract

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

18 pages

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Cited by in corpus (5)

• Group actions on treelike compact spaces
• Quasi-graphs, zero entropy and measures with discrete spectrum
• Disjointness of Möbius from asymptotically periodic functions
• Chowla and Sarnak Conjectures for Kloosterman Sums
• A large class of dendrite maps for which Möbius disjointness property of Sarnak is fulfilled