Higher dimensional Frobenius problem and Lipschitz equivalence of Cantor sets
Higher dimensional Frobenius problem and Lipschitz equivalence of Cantor sets
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具有序结构的自相似集（一）迭代函数系统的空间填充曲线
DOI：
10.1016/j.matpur.2015.05.006
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
张园
中科院分区：
文献类型：
--
作者：
饶辉;张园
之前的一篇论文[Fan等人]引入了更高维度的Frobenius问题。（2015）[8]]。本文研究了Rd中类尘自相似集的Lipschitz等价性。对于任何自相似集，我们与它相关联的高维Frobenius问题，我们表明，相关的高维Frobenius问题的方向增长函数是Lipschitz不变。作为应用，我们解决了当两个尘埃自相似集E和F具有共面比时的Lipschitz等价问题，证明了它们是Lipschitz等价的当且仅当对p，q ≥ 1，E的第p次迭代的压缩向量是F的第q次迭代的压缩向量的置换.这部分回答了法尔科纳和马什（1992）提出的一个问题。
The higher dimensional Frobenius problem was introduced by a preceding paper [Fan et al.(2015)[8]]. In this paper, we investigate the Lipschitz equivalence of dust-like self-similar sets in R d. For any self-similar set, we associate with it a higher dimensional Frobenius problem, and we show that the directional growth function of the associate higher dimensional Frobenius problem is a Lipschitz invariant. As an application, we solve the Lipschitz equivalence problem when two dust-like self-similar sets E and F have coplanar ratios, by showing that they are Lipschitz equivalent if and only if the contraction vector of the p-th iteration of E is a permutation of that of the q-th iteration of F for some p, q≥ 1. This partially answers a question raised by Falconer and Marsh (1992)[7].