反演极限与Lauwerier吸引子(Ⅰ)  

Inverse Limit and Lauwerier Attractor( Ⅰ)

作　　者：郭峰[1] 李登辉[1] 谢建华[1] 

机构地区：[1]西南交通大学力学与工程学院,成都610031

出　　处：《应用数学和力学》2014年第2期212-218,共7页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11172246;11272268)~~

摘　　要：通过研究两维的Lauwerier映射,得到Lauwerier奇怪吸引子的一个解析表达式.研究了二次映射的反演极限空间上移位映射的动力学性质,建立了投影映射,运用反演极限空间理论研究Lauwerier映射,证明了Lauwerier映射限制在其吸引子上与二次映射的反演极限上的移位映射是拓扑半共扼的,从而得到Lauwerier吸引子是Devaney意义下混沌的.A two dimensional Lauwerier mapping was studied and an analytical expression of the strange attractor was obtained. The dynamic properties of the shift map on the inverse limit space of the quadratic mapping were investigated. The projection mapping was established. Then the Lauwerier mapping was studied based on the theory of inverse limit space. It is proved that the Lauwerier mapping restricted to its attractor is topological｜y semi-conjugate to the shift map on the inverse limit space of the quadratic mapping; therefore the Lauwerier strange at- tractor is chaotic in the sense of Devaney.

关 键 词：Lauwerier映射 不稳定流形 奇怪吸引子 反演极限 移位映射 

分 类 号：O189[理学—数学] O313[理学—基础数学]