A NEWALGORITHM FOR COMPUTING ONE-DIMENSIONAL STABLE AND UNSTABLE MANIFOLDS OF MAPS

作者：Li, Huimin^*; Fan, Yangyu; Zhang, Jing

来源：International Journal of Bifurcation and Chaos, 2012, 22(1): 1250018.

DOI：10.1142/S0218127412500186

• Discrete dynamical system
• stable and unstable manifold
• hyperbolic fixed point
• Taylor series
• derivative transportation
• chaotic Henon map

A new algorithm is presented to compute one-dimensional stable and unstable manifolds of fixed points for both two-dimensional and higher dimensional diffeomorphism maps. When computing the stable manifold, the algorithm does not require the explicit expression of the inverse map. The global manifold is grown from a local manifold and one point is added at each step. The new point is located with a "prediction and correction" scheme, which avoids searching the computed part of the manifold with a bisection method and accelerates the searching process. By using the fact that the Jacobian transports derivatives along the orbit of the manifold, the tangent component of the manifold is determined and a new accuracy criterion is proposed to check whether the new point that defines the manifold is acceptable. The performance of the algorithm is demonstrated with several numerical examples.

• 出版日期2012-1
• 单位西北工业大学