Abstract
In this article, let \(\mu \) be a self-conformal measure, we discuss the dimensions of divergence points of self-conformal measures with the open set condition. Our main result is that the set \(\{x\in \mathrm{{{\,\mathrm{supp}\,}}}\mu : A(\frac{\log \mu (B(x,r))}{\log r})=I\}\) is not Taylor fractal and the set \(\{x\in \mathrm{{{\,\mathrm{supp}\,}}}\mu : A(\frac{\log \mu (B(x,r))}{\log r})\subseteq I\}\) is Taylor fractal.
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The third author was supported by NNSF of China (11671208 and 11271191).
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Communicated by H. Bruin.
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Wang, P., Ji, Y., Chen, E. et al. Divergence points of self-conformal measures. Monatsh Math 189, 735–763 (2019). https://doi.org/10.1007/s00605-019-01283-9
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DOI: https://doi.org/10.1007/s00605-019-01283-9