Let $F:(M,\omega) \mapsto (M,\omega)$ be a smooth symplectic diffeomorphism
with a fixed point a and a heteroclinic orbit in the sense of been in the intersection
of the central stable and the central unstable manifolds of
the fixed point.
It is studied the case when the tangent space of a point in
orbit is the direct sum of three subspaces.
The first one is the characteristic
bundle of the central stable manifold of $\mathbf a$
the second one is the characteristic
bundle of the central unstable manifold of $\mathbf a$,
and the third one is tangent to
the intersection of the central stable and unstable manifolds.
In this situation, the homoclinic map $\Lambda$ is a smooth
and symplectic diffeomorphism of open subsets of the central
manifold of $\mathbf a$.
Moreover, if an invariant circle intersects the domain of definition of $\Lambda$ and
its image intersects other circle, there are orbits that
wander from one circle
to the other. This phenomenon is similar to the Arnold
The Melnikov Method gives sufficient conditions for the
existence of homoclinic maps, and non identity homoclinic
maps in a perturbation of a Hamiltonian system.