分形的Kronecker积及其结构特征

详细信息

Kronecker products of fractals and its structural character

摘要: 该文基于矩阵的Kronecker积给出了欧氏空间中两个分形的Kronecker积运算，研究了直线和平面上由表示系统所生成的分形集与自身的Kronecker积的结构特征，通过自然分布原理给出了直线上该类Kronecker积的Hausdorff维数的上界，并证明了其一定包含一个内部非空的区间。
- Hausdorff维数
Abstract: In this paper，it discusses the Kronecker product operation between two fractals in Euclidean space based on the Kronecker product of matrices. We study the structure of the Kronecker product between fractal and itself generated by representation system in line and plane. Further more, we give the upper bound of the Hausdorff dimension of Kronecker product by the Natural distribution principle and prove it must contain a non-empty interval.
- Hausdorff dimension