On the connectedness of planar self-affine sets

Jing-Cheng Liu, Jun Jason Luo and Heng-wen Xie

Chaos, Solitons & Fractals, 2014, vol. 69, issue C, 107-116

Abstract: In this paper, we consider the connectedness of planar self-affine set T(A,D) arising from an integral expanding matrix A with characteristic polynomial f(x)=x2+bx+c and a consecutive collinear digit set D={0,1,…,m}v. The necessary and sufficient conditions only depending on b,c,m are given for the T(A,D) to be connected. Moreover, we also consider the case that D is non-consecutively collinear.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:69:y:2014:i:c:p:107-116

DOI: 10.1016/j.chaos.2014.09.008

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