Packing dimensions of the divergence points of self-similar measures with the open set condition

Xiaoyao Zhou; Ercai Chen

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arXiv · 1203.0095

Packing dimensions of the divergence points of self-similar measures with the open set condition

Xiaoyao Zhou·Ercai Chen

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Abstract

Let $\mu$ be the self-similar measure supported on the self-similar set $K$ with open set condition. In this article, we discuss the packing dimension of the set $\{x\in K: A(\frac{\log\mu(B(x,r))}{\log r})=I\}$ for $I\subseteq\mathbb{R}$, where $A(\frac{\log\mu(B(x,r))}{\log r})$ denotes the set of accumulation points of \frac{\log\mu(B(x,r))}{\log r}$ as $r\searrow0$. Our main result solves the conjecture about packing dimension posed by Olsen and Winter \cite{OlsWin} and generalizes the result in \cite{BaeOlsSni}.

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Xiaoyao Zhou, Ercai Chen. 2012-03-01. Packing dimensions of the divergence points of self-similar measures with the open set condition. https://arxiv.org/abs/1203.0095

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