Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders

Patrick Bernard, K Kaloshin, K Zhang

We prove a form of Arnold diffusion in the a priori stable case. Let H0(p) + $\epsilon$H1($\theta$, p, t), $\theta$ $\in$ T n , p $\in$ B n , t $\in$ T = R/T be a nearly integrable system of arbitr…