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Acta Mathematica Sinica,English Series 2020年第1期36卷 66-76页

作者： Yan Jie TANG Jian Dong YIN Department of Mathematics Nanchang University

The purpose of this paper is to show that for one-sided symbolic systems,there exists an uncountable distributionally scrambled set contained in the set of proper positive upper Banach density recurrent points.

关键词： distributional chaos positive upper Banach density recurrent point one-sided symbolic system

Some Remarks on distributional chaos for Linear Operators

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Communications in Mathematical Research 2011年第4期27卷 307-314页

作者： TIAN GENG Hou BING-ZHE Institution of Mathematics Jilin University Changchun 130012

In this paper, we consider some properties for bounded linear operators concerning distributional chaos. Norm-unimodality of bounded linear operators im- plies distributional chaos. Some properties such as similarity and spectra description for norm-unimodal operators are considered. The existence of distributional chaos in nest algebra is also proved. In addition, we obtain a sufficient and necessary condition of distributional chaos for a class of operators, which contains unilateral backward weighted shift operators.

关键词： distributional chaos norm-unimodality similarity spectrum nest algebra

distributional chaos in Coupled Map Lattices

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Distributional Chaos in Coupled Map Lattices

ON distributional n-chaos

2009中国控制与决策会议

作者： Lidong Wang~1,Bing Li~2,Zhenyan Chu~1 1.Mathematical department,Dalian Nationalities University,dalian 116600,China 2.Mathematical department,Liaoning Normal University,dalian 116029,China

This paper is mainly concerned with coupled map lattice(CML) of the form x+1,n=(1-ε)f(x)+0.5ε{f(x)+f(x)} where f:R→R is a continuous function and m∈N={0,1,…} and n∈Z={…,-1,0,1,…}.A new definition of chaos on recurrent points set in discrete spatiotemporal systems is given and one sufficient condition for this system to be distributionally chaotic is derived.

关键词： Discrete spatiotemporal system Coupled map lattices distributional chaos

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cnki会议

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Acta Mathematica Scientia 2014年第5期34卷 1473-1480页

作者：谭枫符和满 School of the mathematical science South China Normal University College of Mathematics and Information Sciences Zhaoqing University

Let （X, f ） be a topological dynamical system, where X is a nonempty compact and metrizable space with the metric d and f ：X →X is a continuous map. For any integer n≥2, denote the product space by X（n）=X · · · × X｜ {z }n times . We say a system （X, f ） is generally distributionally n-chaotic if there exists a residual set D ？X（n） such that for any point x=（x1, · · · , xn）∈D, lim inf k→∞#（{i：0≤i≤k-1, min{d（fi（xj）, fi（xl））：1≤j 6=l≤n}〈δ0}） k=0 for some real numberδ0〉0 and lim sup k→∞#（{i：0≤i≤k-1, max{d（fi（xj）, fi（xl））：1≤j 6=l≤n}〈δ}） k=1 for any real number δ 〉 0, where #（·） means the cardinality of a set. In this paper, we show that for each integer n ≥ 2, there exists a system （X,σ） which satisfies the following conditions：（1）（X,σ） is transitive;（2）（X,σ） is generally distributionally n-chaotic, but has no distributionally （n＋1）-tuples;（3） the topological entropy of （X,σ） is zero and it has an IT-tuple.

关键词： transitive systems distributional chaos

distributionally scrambled set and minimal set

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Science China Mathematics 2014年第9期57卷 1953-1960页

作者： WANG LiDong WANG Hui Department of Mathematics Dalian Nationalities University School of Mathematical Sciences Dalian University of Technology

We investigate the relation between distributional chaos and minimal sets,and discuss how to obtain various distributionally scrambled sets by using least and simplest minimal *** show:i)an uncountable extremal distributionally scrambled set can appear in a system with just one simple minimal set:a periodic orbit with period 2;ii)an uncountable dense invariant distributionally scrambled set can occur in a system with just two minimal sets:a fixed point and an infinite minimal set;iii)infinitely many minimal sets are necessary to generate a uniform invariant distributionally scrambled set,and an uncountable dense extremal invariant distributionally scrambled set can be constructed by using just countably infinitely many periodic orbits.

关键词： distributional chaos minimal set

A Devaney Chaotic System Which Is Neither Distributively nor Topologically Chaotic

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Communications in Mathematical Research 2013年第2期29卷 148-154页

作者： Chen Zhi-zhi Liao Li Wang Wei Lei Feng-chun Institute of Mathematics Jilin University Institute of Statistics Jilin University of Finance and Economics Institute of Applied Physics and Computational Mathematics

Weiss proved that Devaney chaos does not imply topological chaos and Oprocha pointed out that Devaney chaos does not imply distributional chaos. In this paper, by constructing a simple example which is Devaney chaotic but neither distributively nor topologically chaotic, we give a unified proof for the results of Weiss and Oprocha.

关键词： Devaney chaos distributional chaos topological entropy