Self-similar sets with super-exponential close cylinders

Authors

  • Changhao Chen The Chinese University of Hong Kong, Department of Mathematics

Keywords:

Self-similar sets, exact overlaps, continued fractions

Abstract

 

Baker (2019), Bárány and Käenmäki (2019) independently showed that there exist iterated function systems without exact overlaps and there are super-exponentially close cylinders at all small levels. We adapt the method of Baker and obtain further examples of this type. We prove that for any algebraic number \(\beta\ge 2\) there exist real numbers \(s, t\) such that the iterated function system \(\left \{\frac{x}{\beta}, \frac{x+1}{\beta}, \frac{x+s}{\beta}, \frac{x+t}{\beta}\right \}\) satisfies the above property.
Section
Articles

Published

2021-08-02

How to Cite

Chen, C. (2021). Self-similar sets with super-exponential close cylinders. Annales Fennici Mathematici, 46(2), 727–738. Retrieved from https://afm.journal.fi/article/view/110573