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

Publication date: 30 March 2013

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.

Mathematics Subject Classification ID

Fractals (28A80) Class numbers, class groups, discriminants (11R29)

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