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.
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页码：279 / 303
页数：25
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