一类连通自仿射tiles的性质  

Properties of a Class Connected Self-affine Tiles

作　　者：王飞[1] 

机构地区：[1]长治学院数学系,山西省长治市046011

出　　处：《曲阜师范大学学报（自然科学版）》2012年第1期45-47,共3页Journal of Qufu Normal University(Natural Science)

基　　金：山西省高校科技开发项目(20101130);长治学院科研项目(200909)

摘　　要：自仿射tiles是分形几何中一类重要的集合,在小波理论、数论等学科中有着广泛的应用,文章主要对一类2×2阶下三角矩阵A及数字集D生成的自仿射tiles集T(A,D)进行研究,给出了T(A,D)是连通的必要条件,对进一步研究其它自仿射集的性质具有一定的理论意义,其结论在集合性质的讨论中具有一定的应用价值.Self-affine tiles is a class of important set in fractal geometry, there are extensive applications in wavelet theory and number theory. In this paper, the self-affine tiles T（A, D） generated by a class of 2 ×2 lower triangular matrix A and digit sets D is studied, we give the necessary conditions for T（A, D） to be connected are given, which has theoretical meaning on further studying the properties of other self-affine sets, and its conclusion has some applications in discussing sets properties.

关 键 词：矩阵 自仿射集 自仿射tiles 

分 类 号：O174.4[理学—数学]