- Tytuł:
- Dimension of the intersection of certain Cantor sets in the plane
- Autorzy:
-
Pedersen, Steen
Staw, Vincent T. - Powiązania:
- https://bibliotekanauki.pl/articles/1397337.pdf
- Data publikacji:
- 2021
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
Cantor set
fractal
self-similar
translation
intersection
dimension
Minkowski dimension - Opis:
- In this paper we consider a retained digits Cantor set $T$ based on digit expansions with Gaussian integer base. Let $F$ be the set all $x$ such that the intersection of $T$ with its translate by $x$ is non-empty and let $F_β$ be the subset of $F$ consisting of all $x$ such that the dimension of the intersection of $T$ with its translate by $x$ is $β$ times the dimension of $T$. We find conditions on the retained digits sets under which $F_β$ is dense in $F$ for all $0 ≤ β ≤ 1$. The main novelty in this paper is that multiplication the Gaussian integer base corresponds to an irrational (in fact transcendental) rotation in the complex plane.
- Źródło:
-
Opuscula Mathematica; 2021, 41, 2; 227-244
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł