THE DISTAL AND ASYMPTOTIC SETS FOR CONTINUED FRACTIONS-Reference-Cited by-同舟云学术

THE DISTAL AND ASYMPTOTIC SETS FOR CONTINUED FRACTIONS

Published:2019-12 Issue:08 Volume:27 Page:1950139
ISSN:0218-348X
Container-title:Fractals
language:en
Short-container-title:Fractals

Author:

LIU WEIBIN¹,WANG SHUAILING²^ORCID

Affiliation:

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

2. Department of Mathematics, South China University, of Technology, Guangzhou 510641, P. R. China

Abstract

For continued fraction dynamical system [Formula: see text], we give a classification of the underlying space [Formula: see text] according to the orbit of a given point [Formula: see text]. The sizes of all classes are determined from the viewpoints of measure, Hausdorff dimension and topology. For instance, the Hausdorff dimension of the distal set of [Formula: see text] is one and the Hausdorff dimension of the asymptotic set is either zero or [Formula: see text] according to [Formula: see text] is rational or not.

Funder

MSFC

NSFC

Natural Science Foundation of Guangdong Province

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Geometry and Topology,Modelling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218348X19501391

Reference18 articles.

1. On the Lebesgue Measure of Li-Yorke Pairs for Interval Maps

2. Chaotic and topological properties of β-transformations

3. Li-Yorke pairs of full Hausdorff dimension for some chaotic dynamical systems

4. Chaos for Subshifts of Finite Type

5. The Hausdorff dimension of chaotic sets for interval self-maps

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