| 关于半群作用是spatiotemporal混沌的几点注记 |
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| 引用本文： | 阎欣华,任蕴丽.关于半群作用是spatiotemporal混沌的几点注记[J].北京石油化工学院学报,2011,19(1):58-60. |
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| 作者姓名： | 阎欣华 任蕴丽 |
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| 作者单位： | 阎欣华,Yan Xinhua(北京石油化工学院数理系,北京,102617);任蕴丽,Ren Yunli(河北科技师范学院数理系,秦皇岛,066004) |
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| 基金项目： | 北京市属高等学校人才强教深化计划资助项目;项目号:PHR201008363 |
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| 摘 要： | 混沌理论是动力系统研究的重要课题之一,目前有关一个系统是混沌的定义已有多种,系统在何条件下出现何种混沌是混沌理论研究的一个重要方面。利用Li-Yorke点对,给出了半群作用的spatiotemporal混沌的定义,借助于族以及拓扑等相关知识,讨论混合性、2-刚性和spatio-temporal混沌之间的关系。证明了若(X,T)是拓扑弱混合的且T是交换半群,则系统(X,T)是ST混沌的。
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| 关 键 词： | 拓扑半群 spatiotemporal混沌 弱混合 2-刚性 |
Some Remarks on the Spatiotemporal Chaos Behavior of Semigroup Actions |
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| Yan Xinhua,Ren Yunli.Some Remarks on the Spatiotemporal Chaos Behavior of Semigroup Actions[J].Journal of Beijing Institute of Petro-Chemical Technology,2011,19(1):58-60. |
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| Authors: | Yan Xinhua Ren Yunli |
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| Affiliation: | Yan Xinhua Ren Yunli(1.Department of Mathematics and Physics,Beijing Institute of Petro-chemical Technology,Beijing 102617,China;2.Department of Mathematics and Physics, Hebei Normal University of Science and Technology,Qinhuangdao 066004,China) |
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| Abstract: | Chaos is an important subject in dynamical system research,at present there are various criteria for whether a system is chaotic,and the relationship between chaos and topological properties is an important aspect of chaos theory.Based on Li-Yorke pairs,the definition of spatiotemporal chaos of semigroup actions was given.Using Furstenberg families,we studied the relations among the spatiotemporal chaos,mixing,and 2-rigidity,and we proved that topologically weakly mixing system implies ST chaos. |
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| Keywords: | topological semigroup spatiotemporal chaos weak mixing 2-rigidity |
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