Title:   Mechanism of instability in Hamiltonian Systems: Skipping along a normally hyperbolic invariant manifold

Abstract:
We describe a recent method to show instability in Hamiltonian systems. The mechanism works if some explicit and verifiable transversality conditions are satisfied. The hypothesis can be verified by just checking that some Melnikov type integrals have non-degenerate zeros. This holds for Baire generic sets of perturbations in the C^r topology.
The method uses these hypotheses to conclude the existence of orbits, in near integrable Hamiltonian Systems, which change the action coordinate by a quantity independent of the size of the perturbation.