HAUSDORFF DIMENSION OF UNIVOQUE SETS OF SELF-SIMILAR SETS WITH COMPLETE OVERLAPS-Reference-Cited by-同舟云学术

HAUSDORFF DIMENSION OF UNIVOQUE SETS OF SELF-SIMILAR SETS WITH COMPLETE OVERLAPS

Published:2020-05 Issue:03 Volume:28 Page:2050051
ISSN:0218-348X
Container-title:Fractals
language:en
Short-container-title:Fractals

Author:

GAREEB MOHAMMAD¹^ORCID,LI WENXIA²

Affiliation:

1. Department of Mathematics, East China Normal University, Shanghai 200062, P. R. China

2. Department of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai 200062, P. R. China

Abstract

Let [Formula: see text] and [Formula: see text] an integer. We consider the collection [Formula: see text] of homogeneous self-similar sets on the line such that every two of copies [Formula: see text] of the self-similar set [Formula: see text] are either separated or overlapped with rank [Formula: see text] in [Formula: see text]. For [Formula: see text] generated by [Formula: see text] similitudes, we denote by [Formula: see text] the number of overlaps with rank [Formula: see text]. The set of points in the self-similar set having a unique coding is called the univoque set and denoted by [Formula: see text]. In this paper, we investigate a uniform method to calculate the Hausdorff dimension of the set [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Geometry and Topology,Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218348X20500516

Reference5 articles.

1. Unique expansions of real numbers

2. On the uniqueness of the expansions 333-01333-01333-01

3. Unique Representations of Real Numbers in Non-Integer Bases

4. Estimating the Hausdorff dimensions of univoque sets for self-similar sets