Quantitative almost reducibility and Möbius disjointness for analytic quasiperiodic Schrodinger cocycles

Abstract

Sarnak's Möbius disjointness conjecture states that Möbius function is disjoint to any zero entropy dynamics. We prove that Möbius disjointness conjecture holds for one-frequency analytic quasi-periodic cocycles which are almost reducible, which extend [34,42] to the noncommutative case. The proof relies on quantitative version of almost reducibility.