Möbius disjointness for skew products on a circle and a nilmanifold

Wen Huang; Jianya Liu; Ke Wang

doi:10.3934/dcds.2021006

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2021, Volume 41, Issue 8: 3531-3553. Doi: 10.3934/dcds.2021006

This issue Previous Article Next Article Some results for the large time behavior of Hamilton-Jacobi equations with Caputo time derivative

Möbius disjointness for skew products on a circle and a nilmanifold

1.
CAS Wu Wen-Tsun Key Laboratory of Mathematics & Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China
2.
School of Mathematics & Data Science Institute, Shandong University, Jinan, Shandong 250100, China

^* Corresponding author: Ke Wang
^* Corresponding author: Ke Wang

Received: August 31, 2020

Early access: January 2021

Published: August 2021

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Abstract

Let $ \mathbb{T} $ be the unit circle and $ \Gamma \backslash G $ the $ 3 $-dimensional Heisenberg nilmanifold. We prove that a class of skew products on $ \mathbb{T} \times \Gamma \backslash G $ are distal, and that the Möbius function is linearly disjoint from these skew products. This verifies the Möbius Disjointness Conjecture of Sarnak.

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Mathematics Subject Classification: 37A44, 11L03, 11N37.

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