Arnold Diffusion in Nearly Integrable Hamiltonian Systems and the Geometry of Normally Hyperbolic Invariant Manifolds

We establish the existence of drifting orbits in a priori unstable Hamiltonian systems using the scattering map formalism on normally hyperbolic invariant manifolds. The analysis relies on the transversality of heteroclinic intersections and the geometric properties of the Melnikov potential in high-dimensional phase space.