I was reading this article on the stable and unstable manifolds of an invariant set - http://www.cnbc.cmu.edu/~bard/xppfast/lin2d.html.
It is intutitve that the stable manifold for the stable node (by seeing the figure)is the whole plane but how the unstable manifold of the stable node is the node itself?
Also how to understand the stable and unstable manifolds of the center and the vortex?