Conditional bi-Lipschitz equivalence of self-similar sets

Qi Jia, Chen Chen, Ying Ma, Lei Lei and Kan Jiang

Chaos, Solitons & Fractals, 2021, vol. 153, issue P2

Abstract: Let A,B be two non-empty sets in R. If there exists a bi-Lipschitz map ϕ between A and B, then we say A and B are bi-Lipschitz equivalent. If the function ϕ satisfies some initial extra conditions, for instance, some point in A should be mapped to a particular point in B, then we call ϕ a conditional bi-Lipschitz map. In this paper, we shall consider a class of self-similar sets with touching and overlapping structure, and construct a conditional bi-Lipschitz map between two self-similar sets from this class. Our methodology is different from the graph-directed self-similar sets. As an application, we strengthen the main result of [9].

Keywords: Bi-Lipschitz equivalence; Self-similar sets; Overlaps (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:153:y:2021:i:p2:s096007792100833x

DOI: 10.1016/j.chaos.2021.111479

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