文献类型：会议论文

中文题名：Unstable Manifold of Henon Map

作者：Chen Bo[1];Jia Meng[1];

第一作者：陈波

机构：[1]Department of Electrical Engineering, Xinxiang University, Xinxiang 453000, China;

第一机构：新乡学院机电工程学院

会议论文集：2012 International Conference on Advanced Materials Design and Machanics(2012先进材料设计与机械学国际会议 ICAMDM 2012)论文集

会议日期：20120605

会议地点：厦门

主办单位：TTP

语种：英文

中文关键词：discrete dynamical system;hyperbolic fixed point;unstable manifold

摘要：A new algorithm is presented for computing one dimensional unstable manifold of a map and Henon map is taken as an example to test the performance of the algorithm. The unstable manifold is grown with new point added at each step and the distance between consecutive points is adjusted according to the local curvature. It is proved that the gradient of the manifold at the new point can be predicted by the known points on the manifold and in this way the preimage of the new point could be located immediately. During the simulation, it is found that the unstable manifold of Henon map coincides with its direct iteration when canonical parameters are chosen which means order is obtained out of chaos. In the other several groups of parameters the two branches of the unstable manifolds are nearly symmetric, and they serve as the borderline of the Henon map iteration sequence. We hope that this would contribute to the further exploration of Henon map.