Arnold diffusion in nearly integrable Hamiltonian systems of arbitrary degrees of freedom

Chong-Qing Cheng, Jinxin Xue

Published 2015-03-13Version 1

In this paper, as a continuation of \cite{Ch12}, Arnold diffusion is proved to be a generic phenomenon in nearly integrable convex Hamiltonian systems with arbitrarily many degrees of freedom: $$ H(x,y)=h(y)+\eps P(x,y), \qquad x\in\mathbb{T}^n,\ y\in\mathbb{R}^n,\quad n\geq 3. $$ Under typical perturbation $\eps P$, the system admits "connecting" orbit that passes through any finitely many prescribed small balls in the same energy level $H^{-1}(E)$ provided $E>\min h$.