TY - JOUR
T1 - Connectedness of a Class of Two-Dimensional Self-Affine Tiles Associated with Triangular Matrices
AU - Liu, Jingcheng
AU - Ngai, Sze Man
AU - Tao, Juan
N1 - Publisher Copyright:
© 2015 Elsevier Inc.
PY - 2016/3/15
Y1 - 2016/3/15
N2 - We study the connectedness of planar self-affine sets 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, 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.
AB - We study the connectedness of planar self-affine sets 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, 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.
KW - Connectedness
KW - Digit set
KW - Self-affine tile
UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/354
UR - http://dx.doi.org/10.1016/j.jmaa.2015.10.081
U2 - 10.1016/j.jmaa.2015.10.081
DO - 10.1016/j.jmaa.2015.10.081
M3 - Article
SN - 0022-247X
VL - 435
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
ER -