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.
Recommended Citation
Liu, Jingcheng, Sze-Man Ngai, Juan Tao.
2016.
"Connectedness of a Class of Two-Dimensional Self-Affine Tiles Associated with Triangular Matrices."
Journal of Mathematical Analysis and Applications, 435 (2): 1499-1513.
doi: 10.1016/j.jmaa.2015.10.081
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/354
