  We asymptotically compute the intersection angles between N-dimensional
stable and unstable manifolds in 2N-dimensional symplectic mappings. There
exist particular 1-dimensional stable and unstable sub-manifolds which
experience exponentially small splitting of separatrix in our models. We show
that the angle between the sub-manifolds is exponentially small with respect to
the perturbation parameter $\epsilon$, and the other angles are
$O(\epsilon^2)$.
