Lipschitz Equivalence Class, Ideal Class and the Gauss Class Number Problem
Lipschitz Equivalence Class, Ideal Class and the Gauss Class Number Problem
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发表时间：
2013-03
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通讯作者：
Lifeng Xi;Ying Xiong
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作者：
Lifeng Xi;Ying Xiong
本文研究了bi-Lipschitz映射下自相似集的分类问题，得到了一个重要的bi-Lipschitz不变量，即与IFS相关的环的理想。粗略地说，自相似集的不同Lipschitz等价类对应于相关环的不同理想类。这一结果揭示了分形几何中的Lipschitz分类问题与代数数论中的Gauss类数问题之间的有趣关系。
In this paper, we study the question of classifying self-similar sets under bi-Lipschitz mappings and obtain an important bi-Lipschitz invariant, which is an ideal of a ring related to IFS. Roughly speaking, different Lipschitz equivalence classes of self-similar sets correspond to different ideal classes of a related ring. This result reveals an interesting relationship between the Lipschitz classification problem in fractal geometry and the Gauss class number problem in algebraic number theory.