Selfsimilar sets with superexponential close cylinders
Abstract
S. Baker (2019), B. Bárány and A. Käenmäki (2019) independently showed that there exist iterated function systems without exact overlaps and there are superexponentially close cylinders at all small levels. We adapt the method of S. 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.
 Publication:

arXiv eprints
 Pub Date:
 April 2020
 arXiv:
 arXiv:2004.14037
 Bibcode:
 2020arXiv200414037C
 Keywords:

 Mathematics  Classical Analysis and ODEs;
 Mathematics  Number Theory;
 28A80;
 11J70
 EPrint:
 15 pages