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Growing Unstable Manifolds of Planar Maps

We present a new method for computing the global one-dimensional unstable manifold of a hyperbolic xed point of a map. The key idea is to `grow' the manifold, where the speed of growth is determined only by the curvature of the manifold, and not by the dynamics. In other words, we do not use the standard approach of iterating a fundamental domain. Furthermore, we present two new families of planar maps, that we feel are useful for testing any method for computing unstable manifolds. The performance of our algorithm is illustrated with these two maps, and with the Poincar e map of the driven-damped pendulum.