HAUSDORFF AND HARMONIC MEASURES ON NON-HOMOGENEOUS CANTOR SETS

被引：4

作者：

Batakis, Athanasios ^{[1
]}

Zdunik, Anna ^{[2
]}

机构：

[1] Univ Orleans, MAPMO, F-45067 Orleans 2, France

[2] Univ Warsaw, Inst Math, PL-02097 Warsaw, Poland

来源：

ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA | 2015年 / 40卷 / 01期

关键词：

Harmonic measure; Cantor sets; fractals; Hausdorff dimension; DIMENSION; MAPS; REPELLERS;

D O I：

10.5186/aasfm.2015.4012

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider (not self-similar) Cantor sets defined by a sequence of piecewise linear functions. We prove that the dimension of the harmonic measure on such a set is strictly smaller than its Hausdorff dimension. Some Hausdorff measure estimates for these sets are also provided.

引用

页码：279 / 303

页数：25

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