Abstract: An algorithm for computing 2D stable and unstable manifolds of hyperbolic fixed points of discrete dynamical systems is shown. With the fact that Jacobian transports derivative along orbit of an invariant manifold, an algorithm for computing 1D manifold is proposed. The mesh point is located with a Prediction-Correction scheme which reduces searching time and at the same time gives rise to a simplified accuracy condition. 2D manifold is computed by covering it with orbits of 1D sub-manifold. A generalized Foliation condition is used to guarantee that 2D manifold is growing equally along orbits of 1D sub-manifold in different directions. Performance of the algorithm is demonstrated with hyper chaotic 3D Hénon map and Lorenz system.

Key words: discrete dynamical system, stable manifold, unstable manifold, derivative transportation, 3D Hénon map, Lorenz system, chaotic attractor