The Computation of Unstable Manifolds Using Subdivision and Continuation

Combining the subdivision algorithm for the computation of relative global attractors as described in [1] with a box-oriented continuation technique, we develop a new method for the computation of unstable manifolds. The algorithm creates a covering of the unstable manifold, and it is in principle applicable to invariant manifolds of arbitrary dimension. As an example we compute two-dimensional stable and unstable manifolds in the Lorenz system.