Lipschitz Equivalence Class, Ideal Class and the Gauss Class Number Problem

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.

59 pages, 6 figures

References in corpus (1)

• Ahlfors-David regular sets and bilipschitz maps

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