关于Lozi吸引子结构的讨论  

The Discussion on the Structure of Lozi Attractor

作　　者：郭峰[1] 谢建华[1] 

机构地区：[1]西南交通大学力学与工程学院,四川成都610031

出　　处：《四川师范大学学报（自然科学版）》2014年第2期222-227,共6页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11172246和11272268)资助项目

摘　　要：根据Misiurewicz等对Lozi映射的研究,对该映射的陷阱域的构造过程进行了详细地描述,得到陷阱域G为F的4阶原像和边平行于Df(x)的特征向量的小矩形R的并集.并运用几何理论,形象直观地描述了过鞍点的不稳定流形的动力学性质,从而刻画了奇怪吸引子珚Wu X的复杂结构;而且找到了一个正测度集,其为奇怪吸引子存在的必要条件.In this paper, according to the research of the Lozi mapping studied by Misiurewicz and others, the process of the con- struction for the trapping region is described in great detail. The trapping region G is the setf-4 （F） and a small rectangular R, where the edges of R are parallel to the eigenvector of Df（x）. The dynamic properties of the unstable manifold Wx^u with saddle point X are de- scribed intuitively. The complex structure of the strange attractor Wx^uis depicted. Moreover a positive measure set is found, which is the necessary condition for the existence of the strange attractor.

关 键 词：不稳定流形 吸引域 奇怪吸引子 测度集 

分 类 号：O174.12[理学—数学]