检索结果-南通市图书馆

On the Eventual Shadowing Property and Eventually Shadowable Point of Set-valued Dynamical Systems

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2022年第6期38卷 1105-1115页

作者： Xue Rong XIE jian dong yin Department of Mathematics Nanchang UniversityNanchang 330031P.R.China

The authors introduce the concepts of the eventual shadowing property and eventually shadowable point for set-valued dynamical systems and prove that a set-valued dynamical system has the eventual shadowing property if and only if every point in the phase space is eventually shadowable;every chain transitive set-valued dynamical system has either the eventual shadowing property or no eventually shadowable points;and a set-valued dynamical system admits an eventually shadowable point if and only if it admits a minimal eventually shadowable ***,it is proved that a set-valued dynamical system with the eventual shadowing property is chain mixing if and only if it is mixing and if and only if it has the specification property.

关键词： Eventual shadowing property eventually shadowable point set-valued dynamical system specification

Distributional Chaos Occurring on the Set of Proper Positive Upper Banach Density Recurrent Points of One-sided Symbolic Systems

在线全文

学校读者我要写书评

暂无评论

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

Several Dynamics of Dynamical Systems with the Eventual Shadowing Property

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2023年第10期39卷 1907-1918页

作者： Xue Rong XIE jian dong yin Department of Mathematics Nanchang UniversityNanchang 330031P.R.China

In this article,we provide some sufficient conditions for the dynamical systems with the eventual shadowing property to have positive topological entropy and several equivalent conditions for the dynamical systems wit... 详细信息

关键词： Eventual shadowing property eventually shadowable point topological entropy mixing

An Equivalent Condition for the Self Similar Sets on the Real Line to Have Best Coverings

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2013年第9期29卷 1637-1646页

作者： jian dong yin Zuo Ling ZHOU Department of Mathematics Nanchang University Lingnan College Zhongshan University

In this paper, an equivalent condition for the self similar sets on the real line to have best coverings is given. As a result, it partly gives answer to the conjecture which was posed by Zhou and Feng [Zhou, Z. L., Feng, L.： Twelve open problems on the exact value of the Hausdorff measure and on topological entropy： A brief survey of recent results. Nonlinearity, 17（2）, 493-502 （2004）].

关键词： Self similar set open set condition upper convex density best covering

A Note on Quasi-weakly Almost Periodic Point

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2015年第4期31卷 637-646页

作者： Qi YAN jian dong yin Tao WANG Department of Mathematics Nanchang University

Recently, He et al. [On quasi-weakly almost periodic points. Sci. China Math., 56, 597- 606 （2013）] constructed two binary sub-shifts to solve an open problem posed by Zhou and Feng in [Twelve open problems on the exact value of the Hausdorff measure and on topological entropy： A brief survey of recent results. Nonlinearity, 17, 493-502 （2004）]. In this paper, we study more dynamical properties of those two binary sub-shifts. We show that the first one has zero topological entropy and is transitive but not weakly mixing, while the second one has positive topological entropy and is strongly mixing.

关键词： Topological entropy weakly almost periodic point quasi-weakly almost periodic point,strongly mixing

Several Transitive Properties and Devaney's Chaos

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2016年第3期32卷 373-383页

作者： Tao WANG jian dong yin Qi YAN Department of Mathematics Nanchang University

The relation among transitivity, indecomposability and Z-transitivity is discussed. It is shown that for a non-wandering system （each point is non-wandering）, indecomposability is equivalent to transitivity, and for the dynamical systems without isolated points, Z-transitivity and transitivity are equivalent. Besides, a new transitive level as weak transitivity is introduced and some equivalent conditions of Devaney＇s chaos are given by weak transitivity. Moreover, it is proved that both d- shadowing property and d-shadowing property imply weak transitivity.

关键词： Devaney's chaos indecomposability Z-transitivity weak transitivity

On the Shadowing Property and Shadowable Point of Set-valued Dynamical Systems

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2020年第12期36卷 1384-1394页

作者： Xiao Fang LUO Xiao Xiao NIE jian dong yin Department of Mathematics Nanchang UniversityNanchang 330031P.R.China

In this article,the authors introduce the concept of shadowable points for set-valued dynamical systems,the pointwise version of the shadowing property,and prove that a set-valued dynamical system has the shadowing property iff every point in the phase space is shadowable;every chain transitive set-valued dynamical system has either the shadowing property or no shadowable points;and for a set-valued dynamical system there exists a shadowable point iff there exists a minimal shadowable *** the end,it is proved that a set-valued dynamical system with the shadowing property is totally transitive iff it is mixing and iff it has the specification property.

关键词： Shadowing property shadowable point set-valued dynamical system specification

Banach Upper Density Recurrent Points of C^0-flows

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2016年第11期32卷 1312-1322页

作者： Qi YAN jian dong yin Ballesteros MARNELLIE Wei Ling WU Department of Mathematics Nanchang University

Let X denote a compact metric space with distance d and F ： X×R→ X or Ft ： X→X denote a C0-flow. From the point of view of ergodic theory, all important dynamical behaviors take place on a full measure set. The aim of this paper is to introduce the notion of Banach upper density recurrent points and to show that the closure of the set of all Banach upper density recurrent points equals the measure center or the minimal center of attraction for a C0-flow. Moreover, we give an example to show that the set of quasi-weakly almost periodic points can be included properly in the set of Banach upper density recurrent points, and point out that the set of Banach upper density recurrent points can be included properly in the set of recurrent points.

关键词： C0-flow measure centre weakly almost periodic point quasi-weakly almost periodicpoint Banach upper density recurrent point

An Equivalent Condition for the Self Similar Sets on the Real Line to Have Best Coverings

在线全文

学校读者我要写书评

暂无评论

数学学报（中文版） 2013年第6期56卷 I0001-I0004页

作者： jian dong yin Zuo Ling ZHOU