Local dimensions of self-similar measures satisfying the finite neighbour condition*
Local dimensions of self-similar measures satisfying the finite neighbour condition*
复制标题
满足有限邻域条件的自相似测度的局部维数*
DOI：
10.1088/1361-6544/ac8040
复制
发表时间：
2022
期刊：
影响因子：
1.7
通讯作者：
Hare K
中科院分区：
文献类型：
--
作者：
Hare K
我们研究了R中满足有限邻域条件的自相似测度的局部维集，有限邻域条件形式上强于弱分离条件，但在所有已知的例子中都是满足的。在一个温和的技术假设下，我们证明了可获得的局部维集是(可能是单个的)紧区间的有限并。区间数仅由有限有向图结构的非平凡极大强连通分支的个数限定，仅取决于控制迭代函数系。我们还解释了我们的结果如何允许在许多显式情况下计算局部维集。这是对满足WSC的自相似度量的局部维度集合的大量先前工作的背景和概括。
We study sets of local dimensions for self-similar measures in R satisfying the finite neighbour condition, which is formally stronger than the weak separation condition (WSC) but satisfied in all known examples. Under a mild technical assumption, we establish that the set of attainable local dimensions is a finite union of (possibly singleton) compact intervals. The number of intervals is bounded above by the number of non-trivial maximal strongly connected components of a finite directed graph construction depending only on the governing iterated function system. We also explain how our results allow computations of the sets of local dimensions in many explicit cases. This contextualises and generalises a vast amount of prior work on sets of local dimensions for self-similar measures satisfying the WSC.