%0 Journal Article
%T Growing two-dimensional manifold of nonlinear maps based on generalized Foliation condition<br>基于广义Foliation条件的非线性映射 二维流形计算
%A Li Hui-Min
%A Fan Yang-Yu
%A Sun Heng-Yi
%A Zhang Jing
%A Jia Meng
%A <br>李慧敏
%A 樊养余
%A 孙恒义
%A 张菁
%A 贾蒙
%J 物理学报
%D 2012
%I 
%X In this paper we present an algorithm of computing two-dimensional (2D) stable and unstable manifolds of hyperbolic fixed points of nonlinear maps. The 2D manifold is computed by covering it with orbits of one-dimensional (1D) sub-manifolds. A generalized Foliation condition is proposed to measure the growth of 1D sub-manifolds and eventually control the growth of the 2D manifold along the orbits of 1D sub-manifolds in different directions. At the same time, a procedure for inserting 1D sub-manifolds between adjacent sub-manifolds is presented. The recursive procedure resolves the insertion of new mesh point, the searching for the image (or pre-image), and the computation of the 1D sub-manifolds following the new mesh point tactfully, which does not require the 1D sub-manifolds to be computed from the initial circle and avoids the over assembling of mesh points. The performance of the algorithm is demonstrated with hyper chaotic three-dimensional (3D) Hénon map and Lorenz system.
%K 非线性映射
%K 稳定和不稳定流形
%K 三维Hénon映射
%K Lorenz系统
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=47EA7CFDDEBB28E0&jid=29DF2CB55EF687E7EFA80DFD4B978260&aid=4C92C33EB4B06FC598B70D2F9580FA9A&yid=99E9153A83D4CB11&vid=1D0FA33DA02ABACD&iid=0B39A22176CE99FB&sid=0F7E3C26F0FBB0A0&eid=0F7E3C26F0FBB0A0&journal_id=1000-3290&journal_name=物理学报&referenced_num=0&reference_num=23