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arXiv · 1905.06563

M{ö}bius orthogonality in density for zero entropy dynamical systems

Alexander Gomilko·Mariusz Lemańczyk·Thierry de La Rue
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Abstract

It is proved that whenever a zero entropy dynamical system $(X,T)$ has only countably many ergodic measures and $μ$ stands for the arithmetic M{ö}bius function, then there exists a subset $A$ of integers depending only on the system, of logarithmic density one, such that for each $f$ continuous on $X$, $\frac1N \sum_{n\leq N} f(T^nx)μ(n) \to 0$ as $N\to\infty$, $N\in A$, uniformly in $x\in X$. In particular, the density version of M{ö}bius orthogonality holds.

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Alexander Gomilko, Mariusz Lemańczyk, Thierry de La Rue. 2019-05-16. M{ö}bius orthogonality in density for zero entropy dynamical systems. https://arxiv.org/abs/1905.06563

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