拟弱几乎周期点的等价定义与系统的混沌性  

THE EQUIVALENT DEFINITIONS OF QUASI-WEAKLY ALMOST PERIODIC POINTS AND CHAOS

作　　者：尹建东[1] 周作领[2] 

机构地区：[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

出　　处：《系统科学与数学》2010年第8期1156-1162,共7页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(10971236);江西省自然科学青年基金(2008GQS0071)项目资助

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.In 1992, Zhou Zuoling introduced the notion of weakly almost periodic points. In 1995, Zhou and He Weihong introduced the notion of quasiweakly 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.

关 键 词：传递性 拟弱几乎周期点 Takens—Ruelle混沌. 

分 类 号：O19[理学—数学]