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《ACTA MATHEMATICA SINICA》 1996-03
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Some Dynamical Properties of Continuous Maps on the Warsaw Circle

Xiong Jincheng (Departmeat of Mathematics,South China Normal University, Guangzhou 510631, China)Ye Xiangdong; Zhang Zhiqiang; Huang Jun(Department of Mathematics, University of Science and Technology of China, Hefei 230026, China)  
In the present paper we study the dynamical properties of continuous maps on the Warsaw circle and show that for such a map a theorem similar to the Sarkovskii Theorem for interval maps holds, the closure of the set of periodic points coincides with the closure of the set of recurrent points, the depth of the center is not greater than 4, and the topological entropy is zero if and only if the periods of periodic points are the powers of 2.
【Fund】: 国家自然科学基金
【CateGory Index】: O189.1
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【References】
Chinese Journal Full-text Database 8 Hits
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1 Xiong Jincheng(University of Science and Technology of China);Dynamical Systems of Interval Maps:Nonwandering Set, Topological Entropy and Chaos[J];数学进展;1988-01
【Co-citations】
Chinese Journal Full-text Database 9 Hits
1 Ji Zhanjiang;School of Information and Electronic Engineering,Wuzhou University;;Dynamical Properties of Descendible Mapping on N Dimensional Monomer[J];梧州学院学报;2017-06
2 WANG Li-feng;SHI Yan-ling;Dapartment of Social Science,Nanjing Railway Vocational and Technical College;Basic Department,Yancheng Institute of Technology;;A Necessary and Sufficient Condition of Homoclinic Points for a Self-mapping on the Metric Space[J];淮阴师范学院学报(自然科学版);2015-03
3 ZHAO Yong;The College of mathematics and information,China West Normal University;;The Locus of ■-Limit Point of non- Chaotic Self-Maps on Interval [0,1][J];西华师范大学学报(自然科学版);2015-02
4 LIU Xi-ling;CHEN Liu-qiang;College of Information and Business,Zhongyuan University of Technology;Huanghe Jiaotong University;;Mapping Degree of Self-mapping for Torus in the Topological Space[J];佳木斯大学学报(自然科学版);2015-03
5 LIU Xi-ling;HUO Zhen-hong;CHEN Liu-qing;College of Information and Business,Zhongyuan University of Technology;College of Science,Zhongyuan University of Technology;Zhengzhou Jiaotong Vocational College;;Asymptotic Property of ω-Limit Set Orbit in Self-mapping for Torus[J];长春大学学报;2013-12
6 GENG Xue-ping;JIN Yu-guang;School of Mathematics,Chongqing Normal University;;Strong Invariant Set in Topological Power System[J];重庆工商大学学报(自然科学版);2013-12
7 ZENG Fan-ping;JI Zhan-jiang;ZHANG Geng-rong;College of Mathematics and Information Science,Guangxi University;;Second descendible self-mapping with zero topological entropy[J];广西大学学报(自然科学版);2013-06
8 HUO Zhen-hong;LIU Xi-ling;ZOU Cheng;Department of Mathematics,Zhongyuan University of Technology;College of Information and Business,Zhongyuan University of Technology;Sichuan College of Chemical Technology;;Recurrence Point of Self-mapping for Torus in the Topological Space[J];重庆工商大学学报(自然科学版);2013-10
9 LI Chunxia,JIN Yuguang(College of Mathematics,Chongqing Normal University,Chongqing 400047,China);A little note about several point sets in the metric space[J];周口师范学院学报;2012-05
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1 XIE Jie;JIN Yu-guang;School of Mathematics,Chongqing Normal University;;Several Properties of ω-Limit Set in Topological Space[J];重庆工商大学学报(自然科学版);2014-05
2 NIU Ying-xuan(Dept.of Math.and Phys.,Wanxi College,Lu’an,Anhui 237012,China);Distality and Equicontinuity of Continuous Maps on the Warsaw Circle[J];大学数学;2010-05
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5 Niu Yingxuan(Departmet of Mathematics and Physics,West Anhui University,Anhui Lu'an,237012);Some Dynamical Properties of Continuous Self-maps On Warsaw Circle[J];皖西学院学报;2006-05
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