Suppose we have a saddle fixed point of a map, then we have the stable and unstable manifolds of the saddle points. If the stable and unstable manifolds intersect (If they intersect once they will be intersecting infinite number of times) the map has chaotic behavior.
Now I am thinking what happens if the stable and unstable manifolds come from different fixed points?.
Suppose we have two different fixed points say $P1,P2$ of a map. Now if the unstable manifold of $P1$ intersects the stable manifold of $P2$, then can we say that the map is chaotic?. This is a kind of heteroclinic connection.