On the Separation Structure of Lalley-Gatzouras Fractals

2019/09/27 by Lifeng Xi, Xi, Li-Feng, Jun Jie Miao +3
Computer Science · Mathematics · #FOS: Mathematics #Functional Equations Stability Results #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1909.12468

openalex publication_date 2019/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain a necessary and sufficient condition for Lalley-Gatzouras sets to be uniform disconnected. This enable us to find all Lalley-Gatzouras sets which are quasisymmetrically equivalent to the Cantor ternary set. As another application, we also study the limit behavior of the gap sequence of Lalley-Gatzouras sets.

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