Geodesic
Self-similar sets with super-exponential close cylinders
Changhao Chen1
1 The Chinese University of Hong Kong, Department of Mathematics
Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 727-738.

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  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.
Keywords: Self-similar sets, exact overlaps, continued fractions

Changhao Chen 1

1 The Chinese University of Hong Kong, Department of Mathematics 
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Changhao Chen. Self-similar sets with super-exponential close cylinders. Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 727-738. http://geodesic.mathdoc.fr/item/AFM_2021_46_2_a9/