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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.11087 |
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Table of Contents:
- Let $\mathbb{T}^ω$ be the infinite-dimensional torus, and $T: \mathbb{T}^ω\to \mathbb{T}^ω$ be defined by \[ T: (x_1, x_2, \dots, x_k, \ldots) \mapsto (x_1 + α, x_2 + h(x_1), \dots, x_k + h(x_1 + (k-2)β), \dots) \] with $α\in \mathbb{R}, β\in \mathbb{R}\backslash\mathbb{Q},$ and $h: \mathbb{R}\to \mathbb{R}$ being $1$-period and $C^{1+\varepsilon}$-smooth. This flow $(\mathbb{T}^ω, T)$ is distal, and is also irregular in the sense that its Birkhoff average does not exist for all $x\in \mathbb{T}^ω$. The main result of this paper is that the M öbius Disjointness Conjecture of Sarnak holds for $(\mathbb{T}^ω, T)$.