John Mather (Princeton University)

Arnold diffusion.

Abstract. I will describe work in progress concerning the existence of Arnold diffusion in small Hamiltonian perturbations of integrable systems with positive definite normal torsion. Considering the unperturbed integrable system as the origin in a function space, we show the existence of three open sets U, V, and W in the function space of Hamiltonian systems. The set U is non-void and positively homogeneous. The set V contains an initial segment of every ray r in U emanating from the origin. The set W is open and dense in V. A system in W exhibits Arnold diffusion.