A CONSTRUCTION OF THE SCRAMBLED SET WITH FULL HAUSDORFF DIMENSION FOR BETA-TRANSFORMATIONS-Reference-Cited by-同舟云学术

A CONSTRUCTION OF THE SCRAMBLED SET WITH FULL HAUSDORFF DIMENSION FOR BETA-TRANSFORMATIONS

Published:2018-02 Issue:01 Volume:26 Page:1850005
ISSN:0218-348X
Container-title:Fractals
language:en
Short-container-title:Fractals

Author:

LIU WEI-BIN¹,HUANG CHENG²,LI MEI-HUA²,WANG SHUAILING³

Affiliation:

1. Department of Basic Courses, Guangzhou Maritime University, Guangzhou 510725, P. R. China

2. Faculty of Common Courses, South China Business College, Guangdong University of Foreign Studies, Guangzhou 510545, P. R. China

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

Abstract

For beta-transformations, we prove that the Lebesgue measure of any measurable scrambled set is zero, and there exists a scrambled set with full Hausdorff dimension.

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/S0218348X18500056

Reference21 articles.

1. Representations for real numbers and their ergodic properties

2. On theβ-expansions of real numbers

3. Some metrical theorems in number theory II.

4. Period Three Implies Chaos

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