An invariant set 
is said to be a 
(
)
invariant manifold if 
has the structure of a 
differentiable manifold (Wiggins 1990, p. 14).
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 join up smoothly.
