Quantitative Almost Reducibility and Möbius Disjointness for Analytic Quasiperiodic Schrödinger 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 extends (Liu and Sarnak in Duke Math J 164(7):1353–1399, 2015; Wang in Invent Math 209:175–196, 2017) to the noncommutative case. The proof relies on quantitative version of almost reducibility.

Keywords

Möbius function / Quasi-periodic systems / Almost reducibility / 37E30 / 46L55

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Funding

National Key Research and Development Program of China(2021YFA 1001600)

Tian Yuan Mathematical Foundation(11826102)

National Natural Science Foundation of China(12090012)

National Natural Science Foundation of China(12071232)

Outstanding Youth Foundation of Jiangsu Province of China(BK20200074)

Qinglan Project of Jiangsu Province of China

National Science Foundation(DMS-1753042)

Science Fund for Distinguished Young Scholars of Tianjin(19JCJQJC61300)

Nankai Zhide Foundation

RIGHTS & PERMISSIONS

Peking University