Connectedness of a Class of Two-Dimensional Self-Affine Tiles Associated with Triangular Matrices

Document Type

Article

Publication Date

3-15-2016

Publication Title

Journal of Mathematical Analysis and Applications

DOI

10.1016/j.jmaa.2015.10.081

Abstract

We study the connectedness of planar self-affine sets T(A,D) generated by a matrix of the form View the MathML source together with nonconsecutive and noncollinear digit sets of the form D={l0,l1,…,l|p|−1}×{m0,m1,…,m|q|−1}, where {l0,l1,…,l|p|−1} and {m0,m1,…,m|q|−1} are residue systems for |p| and |q| respectively. We give a necessary and sufficient condition for T(A,D) to be connected, and extend some results by Deng and Lau (2011) [5] to nonconsecutive digit sets.

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