Local dimensions of measures on infinitely generated self-affine sets

被引：7

作者：

Rossi, Eino ^{[1
]}

机构：

[1] Univ Jyvaskyla, Dept Math & Stat, FI-40014 Jyvaskyla, Finland

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2014年 / 413卷 / 02期

关键词：

Self-affine; Infinite iterated function system; Local dimension; ITERATED FUNCTION SYSTEMS; HAUSDORFF DIMENSION; FRACTALS;

D O I：

10.1016/j.jmaa.2013.12.030

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show the existence of the local dimension of an invariant probability measure on an infinitely generated self-affine set, for almost all translations. This implies that an ergodic probability measure is exactly dimensional. Furthermore the local dimension equals the minimum of the local Lyapunov dimension and the dimension of the space. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：1030 / 1039

页数：10

共 50 条

[31] Overlapping self-affine sets
Shmerkin, Pablo
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2006, 55 (04) : 1291 - 1331
[32] Porosity of self-affine sets
Lifeng Xi
[J]. Chinese Annals of Mathematics, Series B, 2008, 29 : 333 - 340
[33] Porosity of self-affine sets
Xi, Lifeng
[J]. CHINESE ANNALS OF MATHEMATICS SERIES B, 2008, 29 (03) : 333 - 340
[34] Planar self-affine sets with equal Hausdorff, box and affinity dimensions
Falconer, Kenneth
Kempton, Tom
[J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2018, 38 : 1369 - 1388
[35] The box dimensions of exceptional self-affine sets in R3
Fraser, Jonathan M.
Jurga, Natalia
[J]. ADVANCES IN MATHEMATICS, 2021, 385
[36] Some Results on Planar Self-Affine Measures with Collinear Digit Sets
Zheng, Jia
Chen, Ming-Liang
[J]. COMPLEX ANALYSIS AND OPERATOR THEORY, 2023, 17 (08)
[37] Some Results on Planar Self-Affine Measures with Collinear Digit Sets
Jia Zheng
Ming-Liang Chen
[J]. Complex Analysis and Operator Theory, 2023, 17
[38] Dimension spectra of self-affine sets
Takahashi, S
[J]. ISRAEL JOURNAL OF MATHEMATICS, 2002, 127 (1) : 1 - 17
[39] Uniform perfectness of self-affine sets
Xie, F
Yin, YC
Sun, YS
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 131 (10) : 3053 - 3057
[40] On the Lipschitz equivalence of self-affine sets
Luo, Jun Jason
[J]. MATHEMATISCHE NACHRICHTEN, 2019, 292 (05) : 1032 - 1042

← 1 2 3 4 5 →