Quantitative almost reducibility and M\"obius disjointness for analytic quasiperiodic Schrodinger cocycles

TL;DR

This paper proves M"obius disjointness for a class of analytic quasiperiodic Schr"odinger cocycles that are almost reducible, extending previous results to the noncommutative setting using quantitative methods.

Contribution

It establishes M"obius disjointness for almost reducible analytic quasiperiodic cocycles, broadening the scope to noncommutative cases.

Findings

M"obius disjointness holds for almost reducible cocycles

Extension of previous results to noncommutative setting

Uses quantitative almost reducibility techniques

Abstract

Sarnak's M\"obius disjointness conjecture states that M\"obius function is disjoint to any zero entropy dynamics. We prove that M\"obius disjointness conjecture holds for one-frequency analytic quasi-periodic cocycles which are almost reducible, which extend \cite{LS15,W17} to the noncommutative case. The proof relies on quantitative version of almost reducibility.