When stable and unstable invariant Manifolds intersect, they do so in a Hyperbolic Fixed Point (Saddle Point). The invariant Manifolds are then called Separatrices. A Hyperbolic Fixed Point is characterized by two ingoing stable Manifolds and two outgoing unstable Manifolds. In integrable systems, incoming and outgoing Manifolds all join up smoothly.

A stable invariant Manifold of a Fixed Point is the set of all points such that the trajectory passing through tends to as .

An unstable invariant Manifold of a Fixed Point is the set of all points such that the trajectory passing through tends to as .

© 1996-9

1999-05-26