We present a general mechanism to establish the existence of diffusing orbits in a large class of nearly integrable Hamiltonian systems. Our approach relies on successive applications of the `outer dynamics' along homoclinic orbits to a normally hyperbolic invariant manifold. The information on the outer dynamics is encoded by a geometrically defined map, referred to as the `scattering map'. We find pseudo-orbits of the scattering map that keep advancing in some privileged direction. Then we use the recurrence property of the `inner dynamics', restricted to the normally hyperbolic invariant manifold, to return to those pseudo-orbits. Finally, we apply topological methods to show the existence of true orbits that follow the successive applications of the two dynamics. This method differs, in several crucial aspects, from earlier works. Unlike the well known `two-dynamics' approach, the method we present relies on the outer dynamics alone. There are virtually no assumptions on the inner 查看全文>>