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arXiv · 2109.01200

Sarnak's conjecture for rank-one subshifts

Mahmood Etedadialiabadi·Su Gao
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Abstract

Using techniques developed in \cite{KLR}, we verify Sarnak's conjecture for two classes of rank-one subshifts with unbounded cutting parameters. The first class of rank-one subshifts we consider are called {\em almost complete congruency classes} ({\em accc}), the definition of which is motivated by the main result of \cite{GS}, which implies that, when a rank-one subshift carries a unique non-atomic invariant probability measure, it is accc if it is measure-theoretically isomorphic to an odometer. The second class we consider consists of Katok's map and its generalizations.

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Mahmood Etedadialiabadi, Su Gao. 2021-09-02. Sarnak's conjecture for rank-one subshifts. https://arxiv.org/abs/2109.01200

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