On Lebesgue Measure of Integral Self-Affine Sets

被引:5
|
作者
Bondarenko, Ievgen V. [1 ]
Kravchenko, Rostyslav V. [2 ]
机构
[1] Natl Taras Shevchenko Univ Kiev, Kiev, Ukraine
[2] Texas A&M Univ, College Stn, TX USA
基金
美国国家科学基金会;
关键词
Self-affine set; Tile; Graph-directed system; Self-similar action; TILES; SYSTEMS; R(N);
D O I
10.1007/s00454-010-9306-8
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
Let A be an expanding integer n x n matrix and D be a finite subset of Z(n). The self-affine set T = T (A, D) is the unique compact set satisfying the equality A(T) = boolean OR(d is an element of D) (T + d). We present an effective algorithm to compute the Lebesgue measure of the self-affine set T, the measure of the intersection T boolean AND (T + u) for u is an element of Z(n), and the measure of the intersection of self-affine sets T (A, D(1)) boolean AND T (A, D(2)) for different sets D(1), D(2) is an element of Z(n).
引用
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页码:389 / 393
页数:5
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