I've been reading a bit around on computation of unstable manifold, which seem to be a big area of research, however no one ever mentions computation of the stable manifold.
Is this because you just reverse time, and then the stable manifold becomes the unstable one, thus computational methods of unstable manifolds also covers computation of stable ones?
Regards,
Stable manifolds are, well, stable under the phase-space flow. Thus, in the most simple case, all you need to do is to integrate forwards in time when you are in the vicinity and you’ll obtain the stable manifold. In some cases (e.g., a quasiperiodic attractor), things may be a bit more difficult, but the gist stays the same.