Self-Affine Tiles Generated by a Finite Number of Matrices

被引：0
|
作者：
Deng, Guotai [1 ,2 ]
Liu, Chuntai [3 ]
Ngai, Sze-Man [4 ,5 ]
机构：
[1] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China
[2] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China
[3] Wuhan Polytech Univ, Sch Math & Comp Sci, Wuhan 430023, Peoples R China
[4] Hunan Normal Univ, Coll Math & Stat, Key Lab High Performance Comp & Stochast Informat, Minist Educ China, Changsha 410081, Hunan, Peoples R China
[5] Georgia Southern Univ, Dept Math Sci, Statesboro, GA 30460 USA
来源：
DISCRETE & COMPUTATIONAL GEOMETRY | 2023年 / 70卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Self-affine tile; Interior Theorem; Tiling set; Reptile; BOUNDARY PARAMETRIZATION; SEPARATION PROPERTIES; CONNECTEDNESS; FRACTALS; TILINGS; PLANE; SETS;
D O I：
10.1007/s00454-023-00529-6
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We study self-affine tiles generated by iterated function systems consisting of affine mappings whose linear parts are defined by different matrices. We obtain an interior theorem for these tiles. We prove a tiling theorem by showing that for such a self-affine tile, there always exists a tiling set. We also obtain a more complete interior theorem for reptiles, which are tiles obtained when the matrices in the iterated function system are similarities. Our results extend some of the classical ones by Lagarias and Wang (Adv. Math. 121(1), 21-49 (1996)), where the IFS maps are defined by a single matrix.
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页码：620 / 644
页数：25
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