RESONANCE BETWEEN SELF-SIMILAR SETS AND THEIR UNIVOQUE SETS

Chen Chen (), Ying Ma (), Lei Lei (), Mohammad Gareeb () and Kan Jiang
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Chen Chen: Department of Mathematics, Ningbo University, P. R. China
Ying Ma: Department of Mathematics, Ningbo University, P. R. China
Lei Lei: Department of Mathematics, Ningbo University, P. R. China
Mohammad Gareeb: ��Department of Mathematics, East China Normal University, P. R. China
Kan Jiang: Department of Mathematics, Ningbo University, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 05, 1-12

Abstract: Let K be a self-similar set in ℠. Generally, if the iterated function system (IFS) of K has some overlaps, then some points in K may have multiple codings. If an x ∈ K has a unique coding, then we call x a univoque point. We denote by 𠒰 (univoque set) the set of points in K having unique codings. In this paper, we shall consider the following natural question: if two self-similar sets are bi-Lipschitz equivalent, then are their associated univoque sets also bi-Lipschitz equivalent. We give a class of self-similar sets with overlaps, and answer the above question affirmatively.

Keywords: Bi-Lipschitz Equivalence; Self-Similar Set; Univoque Set (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21501115

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