Radix expansions and connectedness of planar self-affine fractals

被引：2

作者：

Wang, Lian ^{[1
]}

Leung, King-Shun ^{[2
]}

机构：

[1] Chongqing Univ, Coll Math & Stat, Chongqing 401331, Peoples R China

[2] Educ Univ Hong Kong, Dept Math & Informat Technol, Tai Po, Hong Kong, Peoples R China

来源：

MONATSHEFTE FUR MATHEMATIK | 2020年 / 193卷 / 03期

关键词：

Self-affine set; Connectedness; Radix expansion; Neighbor-generating scheme; TILES;

D O I：

10.1007/s00605-020-01461-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let A be an expanding matrix with characteristic polynomial f (x) = x(2) + px + 3 and D = {0, v, lv + kAv} be a digit set where l, k is an element of Z, v is an element of R-2 so that {v, Av} is linearly independent. It is well known that there exists a unique self-affine fractal T satisfying AT = T + D. In this paper, we give a complete characterization for the connectedness of T by using radix expansion.

引用

页码：705 / 724

页数：20

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