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Topological Entropy of a Graph Map

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Acta Mathematica Sinica,English Series 2018年第2期34卷 194-208页

作者： Tai Xiang SUN Guangxi Key Laboratory Cultivation Base of Cross-border E-commerce Intelligent Information Processing Guangxi University of Finance and Economics

Let G be a graph and f： G → G be a continuous map. Denote by h（f）, P（f）, AP（f）, R（f） and w（x, f） the topological entropy of f, the set of periodic points of f, the set of almost periodic points of f, the set of recurrent points of f and the w-limit set of x under f, respectively. In this paper, we show that the following statements are equivalent：（1） h（f）〉 O. （2） There exists an x ∈ G such that w（x, f） ∩ P（f） ≠θ and w（x, f） is an infinite set. （3） There exists an x ∈ G such that w（x, f） contains two minimal sets. （4） There exist x, y ∈G such that w（x, f） - w（y, f） is an uncountable set andw（y,f）∩w（x,f）≠θ. （5） There exist anx C Gand a closed subset A w（x,f） with f（A） A such that w（x,f） - A is an uncountable set. （6） R（f） - nP（f） ≠θ. （7） f｜P（f） is not pointwise equicontinuous.

关键词： Topological entropy periodic point w-limit set recurrent point

CHAOS AND ORDER OF INVERSE LIMIT SPACE FOR A GRAPH MAP

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Chinese Annals of Mathematics,Series B 2000年第1期21卷 25-32页

作者： LUJIE DepartmentofMathematics SouthChinaNormalUniversityGuangzhou510631China

With the method of inverse limit, the author obtains several criteria of chaos of piecewise monotone continuous maps on finite graphs.

关键词： Chaos Inverse limit Order recurrent point

Special α-limit points and unilateral γ-limit points for graph maps

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Science China Mathematics 2011年第9期54卷 2013-2018页

作者： SUN TaiXiang XI HongJian LIANG HaiLan College of Mathematics and Information Science Guangxi University Nanning 530004 China Department of Mathematics Guangxi College of Finance and Economics Nanning 530003 China

Let G be a graph and f ： G → G be a continuous map. Denote by P（f）, R（f）, SA（f） and UF（f） the sets of periodic points, recurrent points, special α-limit points and unilateral γ-limit points of f, respectiv... 详细信息

关键词： graph map recurrent point periodic point special α-limit point unilateral γ-limit point

NON-WANDERING SET OF A CONTINUOUS GRAPH MAP

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Applied Mathematics(A Journal of Chinese Universities) 2003年第4期18卷 477-481页

作者： GuRongbao SunTaixiang ZhengTingting Dept.ofAppl.Math. NanjingUniv.ofFinanceandEconomicsNanjing210003China Dept.ofMath. AnhuiUniv.Hefei230039China Dept.ofMath. GuangxiUniv.Nanning530004China

The non-wandering set Ω(f) for a graph map f is investigated. It is showed that Ω(f) is contained in the closure of the set ER(f) of eventually recurrent points of f and ω-limit set ω(Ω(f)) of Ω(f) is containe... 详细信息

关键词： graph map recurrent point eventually recurrent point ω-limit set non-wandering set

THE LIMIT SET OF A CONTINUOUS SELF-MAP OF THE TREE

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Annals of Differential Equations 2003年第1期19卷 60-64页

作者：罗智明张可村 Science College Xi'an Jiaotong University Xi'an 710049 Dept. of Information Hunan Business College Changsha 410205 Science College Xi'an Jiaotong University Xi'an 710049 Let f denote a continuous map of a tree T to itself. A point x ∈T is called a 7-limit point of f if it is both an ω-limit point and an α-limit point. In the present paper we show that (1) Ω-Γis countable (2) A -Γand P - Γare either empty or countably infinite where P denotes the closure of the set of periodic points P.

Let f denote a continuous map of a tree T to itself. A point x ∈ T is called a 7-limit point of f if it is both an ω-limit point and an α-limit point. In the present paper, we show that (1) Ω-Γ is countable, (2) A -Γ and P - Γ are either empty or countably infinite, where P denotes the closure of the set of periodic points P.

关键词： nonwandering point recurrent point one-side isolated

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具有伪轨跟踪性质的逐点回归动力系统

Northeastern Mathematical Journal 1996年第1期12卷 73-78页

作者：麦结华

Let X be a metric space,and F:X×R→X α C0-flow on *** is proved in this peper that if every point in X is a positively or negatively recurrent(Posisson stable) point of F,and F has the pseudo-orbit tracing property,then every chain-connected component of X is a minimal set of *** follows from this that each pointwise recurrent C0-flow on a Chain-connected space having the pseudoorbit tracing property must be a minimal flow,i.e.,the whole space must be a (unique) minimal set of *** the discrete semi-flow generated by a continuous map f:X→*** results are also given.

关键词： recurrent point Pseudo-orbit Tracing Property Minimal Set recurrent Orbit.Chain-connected Space Almost Periodic point