一族随机自相似迭代函数系统的维数性质
Dimension properties of a family of random self-similar iterated function systems
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中文总结 AI 辅助
本文针对一类具有良好组织重叠结构的随机自相似集，基于期望矩阵的压力函数给出了其维数公式，并推广了非均匀海绵体的有理投影。
中文摘要 AI 辅助
本文给出了某些随机化自相似集的维数公式。所考虑的自相似集是非均匀海绵体的有理投影的$d$维推广：它们存在重叠，但重叠结构在某种意义上是良好组织的。随机化根据与IFS柱体对应的带标记的Galton-Watson树进行，例如在曼德勃罗渗透集的情形中。维数公式由对应于期望矩阵的压力函数给出，该函数描述了系统的重叠结构和随机性。
英文摘要
In this note we present a dimension formula for certain randomized self-similar sets. The self-similar sets we are considering are $d$-dimensional generalizations of rational projections of inhomogeneous sponges: they have overlaps, but the overlapping structure is in some sense well-organized. The randomization happens according to a labelled Galton-Watson tree corresponding to the cylinders of the IFS, for example as in the case of the Mandelbrot percolation set. The dimension formula is given in terms of a pressure function corresponding to the expectation matrices, which describes the overlapping structure and the randomness of the system.
发表机构
- Budapest University of Technology and Economics（布达佩斯技术与经济大学）
- HUN-REN Alfréd Rényi Institute of Mathematics（匈牙利研究网络阿尔弗雷德·雷尼数学研究所）
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