A characterization of connected self-affine fractals arising from collinear digits

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:456

Article

Leung, King-Shun¹  Luo, Jun Jason² 

[1] Educ Univ Hong Kong, Dept Math & Informat Technol, Hong Kong, Hong Kong, Peoples R China

[2] Chongqing Univ, Coll Math & Stat, Chongqing 401391, Peoples R China

关键词: Connectedness;    Self-affine fractal;    Collinear digit;    Radix expansion;   

DOI  :  10.1016/j.jmaa.2017.07.008

来源: Elsevier

【 摘 要 】

Let A be an expanding integer matrix with characteristic polynomial f(x) = x(2) - + px + q, and let D = {0,1,, vertical bar q vertical bar - 2, vertical bar q vertical bar + m}v be a collinear digit set where m >= 0, v is an element of Z(2). It is well known that there exists a unique self-a.ffine fractal T satisfying AT = T + D. In this paper, we give a complete characterization of connectedness of T. That generalizes the previous result for vertical bar q vertical bar = 3. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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