几个特殊的混沌集  

Several Special Scrambled Sets

作　　者：周雷[1] 

机构地区：[1]上海工程技术大学基础教学学院,上海201620

出　　处：《上海工程技术大学学报》2007年第4期294-296,共3页Journal of Shanghai University of Engineering Science

基　　金：上海高校选拔培养优秀青年教师科研专项基金资助项目(06XPYQ41)

摘　　要：目前,混沌在各学科中被广泛应用。许多数学家构造出具有不同性质的混沌集,这为其他学科对混沌的应用打下了良好的基础。以圆盘上特殊的旋转映射为工具,构造出圆盘上一些有趣的混沌函数,它们的混沌集具有不同的性质。如除圆心外均为混沌点;混沌集与周期点集可以分列在不同的区域。作为应用,说明了Li-Yorke混沌定义中的第3个条件是不必要的。Chaos has been applied extensively at present. Mathematicians have construc sets possessing different properties, which provide great convenience to apply chaotic in ted many scrambled other fields. In this paper, several interesting scrambled sets possessing different properties were constructed with the rotation in discs. Their properties include that, （1） all points except the center of the disc are scrambled points, （2） the scrambled sets and the set of period points distribute in the different areas. It was explained that the condition （3） in the definition of Li-Yorke chaos is unnecessary.

关 键 词：混沌集 开圆盘 周期点集 旋转 Li—Yorke混沌 

分 类 号：O19[理学—数学] O189.11[理学—基础数学]