Lipschitz Equivalence Class, Ideal Class and the Gauss Class Number Problem
Metric Geometry
2013-04-19 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1304.0103,
title = {Lipschitz Equivalence Class, Ideal Class and the Gauss Class Number Problem},
author = {Li-Feng Xi and Ying Xiong},
journal= {arXiv preprint arXiv:1304.0103},
year = {2013}
}
Comments
59 pages, 6 figures