Multi-Model Cantor Sets

Details Multi-Model Cantor Sets Multi-Model Cantor Sets

2002-02-19

arxiv.org/abs/math/0202198v1

Mathematics

Dynamical Systems

26 pages, 10 figures

Scientific paper

In this paper we define a new class of metric spaces, called multi-model Cantor sets. We compute the Hausdorff dimension and show that the Hausdorff measure of a multi-model Cantor set is finite and non-zero. We then show that a bilipschitz map from one multi-model Cantor set to another has constant Radon-Nikodym derivative on some clopen. We use this to obtain an invariant up to bilipschitz homeomorphism.

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