提出了一种基于曲率约束条件的计算离散动力系统鞍型不动点一维不稳定流形的新算法,并以Hénon映射为例进行了计算.新算法以增长流形为基本思想,通过曲率约束和距离控制来确定离散点间的距离;提出流形的偏转角度可以通过流形上的已知点来预测,解决了流形上新点的原像位置快速确定的困难.仿真发现:Hénon映射的一维不稳定流形在标准参数下与Hénon映射产生的散点图分布一致,在其它几组参数下,一维不稳定流形的两个分支之间保持着某种程度的对称性,该研究对Hénon映射的进一步研究打下基础.%A new algorithm was presented for computing one dimensional unstable manifold for saddle fixed point of a discrete dynamic system based on the constraint condition of curvature.Hénon map was taken as an example to check the performance of the algorithm.The manifold growing was taken as the basic idea of the new algorithm.Curvature constraint and distance control were used to determine the distance between discrete points.The unstable manifold grew with new point added at each step and the distance between consecutive points was adjusted according to the local curvature.It was proved that the gradient of the manifold at the new point can be predicted with the known points on the manifold and in this way the preimage of the new point can be located immediately.The simulation showed that the one dimensional unstable manifold of Hénon map coincides with the scatter point diagram distribution produced by itself under standard parameters;under the other several groups of parameters,two branches of the unstable manifold are nearly symmetric,and they serve as the borderline of Hénon map iteration sequence.The results laid a foundation for further studying H6non map.
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