Divergence points of self-conformal measures

  • Pei Wang
  • Yong JiEmail author
  • Ercai Chen
  • Yaqing Zhang


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.


Self-conformal measure Divergence points Moran structrue Dimension Open set condition 

Mathematics Subject Classification




The third author was supported by NNSF of China (11671208 and 11271191).


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Basic Teaching DepartmentNanjing University Jinling CollegeNanjingPeople’s Republic of China
  2. 2.School of Mathematical Sciences and Institute of MathematicsNanjing Normal UniversityNanjingPeople’s Republic of China

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