RUN-LENGTH FUNCTION FOR REAL NUMBERS IN β-EXPANSIONS-Reference-Cited by-同舟云学术

RUN-LENGTH FUNCTION FOR REAL NUMBERS IN β-EXPANSIONS

Published:2022-04-25 Issue:03 Volume:30 Page:
ISSN:0218-348X
Container-title:Fractals
language:en
Short-container-title:Fractals

Author:

ZHENG LIXUAN¹^ORCID,WU MIN²^ORCID

Affiliation:

1. Department of Statistics and Mathematics, Guangdong University of Finance and Economics, 510320 Guangzhou, P. R. China

2. Department of Mathematics, South China University of Technology, 510640 Guangzhou, P. R. China

Abstract

Let [Formula: see text] and [Formula: see text] be two real numbers. For all [Formula: see text], the run-length function with respect to [Formula: see text], denoted by [Formula: see text], is defined as the maximal length of the prefix of the [Formula: see text]-expansion of [Formula: see text] amongst the first [Formula: see text] digits of the [Formula: see text]-expansion of [Formula: see text]. The level set [Formula: see text] is investigated in our paper. We obtain the Hausdorff dimension of [Formula: see text] which extends many known results on run-length function in [Formula: see text]-expansions.

Funder

Guangzhou Natural Science Foundation

National Natural Science Foundation of China

Natural Science Foundation of Guangdong Province

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Geometry and Topology,Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218348X22500335

Reference19 articles.

1. Representations for real numbers and their ergodic properties

2. On theβ-expansions of real numbers

3. β-Expansions and symbolic dynamics

4. Distribution of full cylinders and the Diophantine properties of the orbits in $\beta$-expansions