| 拟弱几乎周期点的等价定义与系统的混沌性 |
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| 引用本文： | 尹建东,周作领.拟弱几乎周期点的等价定义与系统的混沌性[J].系统科学与数学,2010,30(8):1156-1162. |
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| 作者姓名： | 尹建东 周作领 |
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| 作者单位： | 1. 南昌大学理学院数学系,南昌,330031
2. 中山大学岭南学院,广州,510275 |
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| 基金项目： | 国家自然科学基金，江西省自然科学青年基金 |
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| 摘 要： | 1992年, 周作领引进了弱几乎周期点这一概念. 1995年, 周和何伟弘又引进了拟弱几乎周期点这个概念, 并利用它们深刻地刻画了一个动力系统的本质所在. 为了更好地看出这两者的区别,首先从回复时间集的角度给出拟弱几乎周期点的等价定义,然后研究了一个存在真的拟弱几乎周期点的系统的混沌情况,得到了这样的系统是Takens-Ruelle混沌的.
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| 关 键 词： | 传递性 拟弱几乎周期点 Takens-Ruelle混沌. |
| 收稿时间： | 2009-11-30 |
| 修稿时间： | 2010-7-12 |
THE EQUIVALENT DEFINITIONS OF QUASI-WEAKLY ALMOST PERIODIC POINTS AND CHAOS |
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| YIN Jiandong,ZHOU Zuoling.THE EQUIVALENT DEFINITIONS OF QUASI-WEAKLY ALMOST PERIODIC POINTS AND CHAOS[J].Journal of Systems Science and Mathematical Sciences,2010,30(8):1156-1162. |
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| Authors: | YIN Jiandong ZHOU Zuoling |
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| Institution: | Department of Mathematics, Nanchang University, 330031; Lingnan School, Zhongshan University, 510275 |
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| Abstract: | In 1992, Zhou Zuoling introduced the notion of weakly almost periodic points. In 1995, Zhou and He Weihong introduced the notion of quasi- weakly almost periodic points to reveal the essence of a dynamical system. In order to distinguish them more clearly, the equivalent definitions of them are given in the paper. At the end of this paper, the chaotic property of a transitive dynamical system is studied, in which there is a transitive quasi weakly almost periodic point but there is no weakly almost periodic one, and such system is Takens-Ruelle chaos system. |
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| Keywords: | Transitive property Quasi-weakly almost periodic points Takens-Ruelle chaos |
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