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

Voir la notice de l'article provenant de la source Journal.fi

  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 
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/
@article{AFM_2021_46_2_a9,
     author = {Changhao Chen},
     title = {Self-similar sets with super-exponential close cylinders},
     journal = {Annales Fennici Mathematici},
     pages = {727--738},
     year = {2021},
     volume = {46},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AFM_2021_46_2_a9/}
}
TY  - JOUR
AU  - Changhao Chen
TI  - Self-similar sets with super-exponential close cylinders
JO  - Annales Fennici Mathematici
PY  - 2021
SP  - 727
EP  - 738
VL  - 46
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/AFM_2021_46_2_a9/
LA  - en
ID  - AFM_2021_46_2_a9
ER  - 
%0 Journal Article
%A Changhao Chen
%T Self-similar sets with super-exponential close cylinders
%J Annales Fennici Mathematici
%D 2021
%P 727-738
%V 46
%N 2
%U http://geodesic.mathdoc.fr/item/AFM_2021_46_2_a9/
%G en
%F AFM_2021_46_2_a9