Dimension of Slices Through Fractals with Initial Cubic Pattern  

作　　者：Lifeng XI Wen WU Ying XIONG 

机构地区：[1]Department of Mathematics,Ningbo University,Ningbo 315211,Zhejiang,China [2]School of Mathematics,South China University of Technology,Guangzhou 510641,China

出　　处：《Chinese Annals of Mathematics,Series B》2017年第5期1145-1178,共34页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.11371329,11471124,11071090,11071224,11101159,11401188);K.C.Wong Magna Fund in Ningbo University,the Natural Science Foundation of Zhejiang Province(Nos.LR13A010001,LY12F02011);the Natural Science Foundation of Guangdong Province(No.S2011040005741)

摘　　要：In this paper, the Hausdorff dimension of the intersection of self-similar fractals in Euclidean space R^n generated from an initial cube pattern with an(n-m)-dimensional hyperplane V in a fixed direction is discussed. The authors give a sufficient condition which ensures that the Hausdorff dimensions of the slices of the fractal sets generated by "multirules" take the value in Marstrand's theorem, i.e., the dimension of the self-similar sets minus one. For the self-similar fractals generated with initial cube pattern, this sufficient condition also ensures that the projection measure μVis absolutely continuous with respect to the Lebesgue measure L^m. When μV《 L^m, the connection of the local dimension ofμVand the box dimension of slices is given.

关 键 词：SLICE Self-similar set DIMENSION FRACTAL 

分 类 号：O189[理学—数学]