We will address the problem of computing a two-dimensional global stable or unstable manifold of a hyperbolic equilibrium. We focus on the technique to grow the manifold as a collection of levelsets that are defined as the sets of points with equal geodesic distances to the equilibrium (along the manifold). Even though this method has restrictions, so far we did not encounter these in practice. For the purpose of demonstration, we present a constructed example to explain

these limitations.

Already in a three-dimensional phase space it may be hard to visualise the results. We will briefly show some new ideas that are useful when the manifold has a complicated geometry, such as, for example, the stable manifold of the origin in the Lorenz system.

This is joint work with Bernd Krauskopf (Bristol).