DIMENSION OF INVARIANT MEASURES FOR AFFINE ITERATED FUNCTION SYSTEMS

被引：12

作者：

Feng, De-Jun ^{[1
]}

机构：

[1] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China

来源：

DUKE MATHEMATICAL JOURNAL | 2023年 / 172卷 / 04期

关键词：

LEDRAPPIER-YOUNG FORMULA; HAUSDORFF DIMENSION; EQUILIBRIUM STATES; EQUAL HAUSDORFF; ERGODIC-THEORY; SELF; ENTROPY; SETS; PROJECTIONS; CONTINUITY;

D O I：

10.1215/00127094-2022-0014

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let {SiIi2 integral be a finite contracting affine iterated function system (IFS) on Rd. Let (E, a) denote the two-sided full shift over the alphabet A, and let n : E ! Rd be the coding map associated with the IFS. We prove that the projection of an ergodic a-invariant measure on E under n is always exact dimensional, and its Haus-dorff dimension satisfies a Ledrappier-Young-type formula. Furthermore, the result extends to average contracting affine IFSs. This completes several previous results and answers a folklore open question in the community of fractals. Some applications are given to the dimension of self-affine sets and measures.

引用

页码：701 / 774

页数：74

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