The Moebius function and continuous extensions of rotations

2013/10/09 by Joanna Kułaga-Przymus, Mariusz Lemańczyk, Kułaga-Przymus, Joanna +1
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.DS

paper · pdf · doi:10.48550/arxiv.1310.2546

26 pages. The paper has been shortened. It covers now only compact group extensions of rotations, Rokhlin extensions have been removed. A remark on disjointness criterion for irrational rotation was added

openalex publication_date 2013/10/09 · arxiv created 2014/08/05 · arxiv updated 2014/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f\colon \mathbbT→ ℝ be of class C^1+δ for some δ>0 and let c∈ℤ. We show that for a generic α∈ℝ, the extension T_c,f\colon \mathbbT²→\mathbbT² of the irrational rotation Tx=x+α, given by T_c,f(x,u)=(x+α, u+cx+f(x)) (\bmod 1) satisfies Sarnak's conjecture.

Citations

• Ergodicity of Rokhlin cocycles

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