Equidistribution results for self-similar measures

Abstract: A well known theorem due to Koksma states that for Lebesgue almost every $x>1$ the sequence $(x^n)$ is uniformly distributed modulo one. In this talk I will discuss an analogue of this statement that holds for fractal measures. As a corollary of this result we show that if $C$ is equal to the middle third Cantor set and $t\geq 1$, then almost every $x\in C+t$ is such that $(x^n)$ is uniformly distributed modulo one. Here almost every is with respect to the natural measure on $C+t$.

dynamical systemsnumber theory

Audience: researchers in the topic

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One World Numeration seminar

Series comments: Description: Online seminar on numeration systems and related topics

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