Affiliation:
1. The College of Science, Northwest A&F University, Yangling, Shannxi 712100, P. R. China
Abstract
Given an integer n ≥ 2 and an ordered pair (A, B) with A ⊂ {k1α + k2β : k1 + k2 ≤ n - 1 and k1, k2 ∈ ℕ ∪{0}} and B ⊂ {k1α + k2β : 2 ≤ k1 + k2 ≤ n and k1, k2 ∈ ℕ}, where [Formula: see text]. Let T ≔ T(A, B) be unique compact set of ℝ2 satisfying the set equation: T = [(T+A)∪(B-T)]/n. In this paper, we show that such self-similar sets which are totally disconnected are determined to within Lipschitz equivalence by their Hausdorff dimension.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Geometry and Topology,Modeling and Simulation
Cited by
3 articles.
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