MULTIFRACTAL DECOMPOSITIONS OF MORAN FRACTALS

被引：233

作者：

CAWLEY, R ^{[1
]}

MAULDIN, RD ^{[1
]}

机构：

[1] UNIV N TEXAS,DEPT MATH,DENTON,TX 76203

来源：

ADVANCES IN MATHEMATICS | 1992年 / 92卷 / 02期

关键词：

D O I：

10.1016/0001-8708(92)90064-R

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present a rigorous construction and generalization of the multifractal decomposition for Moran fractals with infinite product measure. The generalization is specified by a system of nonnegative weights in the partition sum. All the usual (smooth) properties of the f(α) theory are recovered for the case that the weights are equal to unity. The generalized spectrum, f(α, w), is invariant to a group of gauge transformations of the weights, and, in addition, need no longer be concave. In case the fractal is a Cantor set generated by an iterated function system of similarities, α is the pointwise dimension of the measure. We discuss properties of some examples. © 1992.

引用

页码：196 / 236

页数：41

共 32 条

[1] ITERATED FUNCTION SYSTEMS AND THE GLOBAL CONSTRUCTION OF FRACTALS [J].