Ledrappier-Young formula and exact dimensionality of self-affine measures
Ledrappier-Young formula and exact dimensionality of self-affine measures
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DOI：
10.1016/j.aim.2017.07.015
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发表时间：
2015-11
影响因子：
1.7
通讯作者：
Bal'azs B'ar'any;A. Kaenmaki
中科院分区：
文献类型：
--
作者：
Bal'azs B'ar'any;A. Kaenmaki
在本文中，我们解决了平面上自仿射测度的精确维数这一长期存在的开放性问题。我们证明，无论定义迭代函数系统的选择如何，平面上的每个自仿射测量都是精确的维度。在更高的维度中，在某些假设下，我们证明自仿射和准自仿射测度是精确维度的。在这两种情况下，测量值都满足 Ledrappier-Young 公式。
In this paper, we solve the long standing open problem on exact dimensionality of self-affine measures on the plane. We show that every self-affine measure on the plane is exact dimensional regardless of the choice of the defining iterated function system. In higher dimensions, under certain assumptions, we prove that self-affine and quasi self-affine measures are exact dimensional. In both cases, the measures satisfy the Ledrappier–Young formula.