We will prove Sarnak’s conjecture on Möbius disjointness for continuous interval maps of zero entropy and also for orientation-preserving circle homeomorphisms by reducing these result to a well-known theorem of Davenport from 1937.
The author would like to express his gratitude to Ana Rodrigues for proposing the problem and for useful comments on the manuscript, and to Michael Benedicks for his guidance and many valuable suggestions. I also want to thank Lennart Carleson for his suggestion to consider circle homeomorphisms that are only semi-conjugate to rotations.
"On Möbius orthogonality for interval maps of zero entropy and orientation-preserving circle homeomorphisms." Ark. Mat. 53 (2) 317 - 327, October 2015. https://doi.org/10.1007/s11512-014-0208-5