Quantitative Almost Reducibility and Möbius Disjointness for Analytic Quasiperiodic Schrödinger Cocycles
Quantitative Almost Reducibility and Möbius Disjointness for Analytic Quasiperiodic Schrödinger Cocycles
复制标题
DOI：
10.1007/s42543-023-00081-5
复制
发表时间：
2021-11
期刊：
影响因子：
--
通讯作者：
Wen-ling Huang;Jing Wang;Zhiren Wang;Qi Zhou
中科院分区：
文献类型：
--
作者：
Wen-ling Huang;Jing Wang;Zhiren Wang;Qi Zhou
沙纳克的莫比乌斯不相交猜想指出莫比乌斯函数与任何零熵动力学都不相交。我们证明了Möbius不相交性猜想对于几乎可约的单频解析拟周期上圈成立，这将（Liu和Sarnak in杜克数学J 164（7）：1353-1399，2015; Wang in Invent Math 209：175-196，2017）扩展到非交换的情况。证明依赖于几乎可约化的定量形式。
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.