On the connectedness of self-affine tiles

被引：64

作者：

Kirat, I ^{[1
]}

Lau, KS

机构：

[1] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA

[2] Chinese Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China

来源：

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 2000年 / 62卷

关键词：

D O I：

10.1112/S002461070000106X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let Tbe a self-affine tile in R-n defined by an integral expanding matrix A and a digit set D. The paper gives a necessary and sufficient condition for the connectedness of T. The condition can be checked algebraically via the characteristic polynomial of A. Through the use of this, it is shown that in R-2, for any integral expanding matrix A, there exists a digit set D such that the corresponding tile Tis connected. This answers a question of Bandt and Gelbrich. Some partial results for the higher-dimensional cases are also given.

引用

页码：291 / 304

页数：14

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