Title: Topological methods for instability and diffusion in Hamiltonian systems

Abstract: We investigate instability and diffusion in some particular Hamiltonian systems through topological methods. The models considered contain a normally hyperbolic manifold. There exist almost invariant tori on the normally hyperbolic manifold. Those tori are whiskered tori for the full system and exhibit heteroclinic connections. The global dynamics is analyzed through the interplay between the dynamics restricted to the normally hyperbolic manifold and the dynamics given by the homoclinic excursions. We use a topological technique based on correctly aligned windows to prove the existence of diffusing orbits. Our method does not use the KAM theorem, and so it requires lower differentiability conditions than some current proofs. We also provide an estimate of the diffusion time.