Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4614548 | Journal of Mathematical Analysis and Applications | 2016 | 15 Pages |
Abstract
We study the connectedness of planar self-affine sets T(A,D)T(A,D) generated by a matrix of the form A=[p0−aq] together with nonconsecutive and noncollinear digit sets of the form D={l0,l1,…,l|p|−1}×{m0,m1,…,m|q|−1}D={l0,l1,…,l|p|−1}×{m0,m1,…,m|q|−1}, where {l0,l1,…,l|p|−1}{l0,l1,…,l|p|−1} and {m0,m1,…,m|q|−1}{m0,m1,…,m|q|−1} are residue systems for |p||p| and |q||q| respectively. We give a necessary and sufficient condition for T(A,D)T(A,D) to be connected, and extend some results by Deng and Lau (2011) [5] to nonconsecutive digit sets.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Jingcheng Liu, Sze-Man Ngai, Juan Tao,