Arnold diffusion in nearly integrable Hamiltonian systems

School of Mathematics Colloquium
Thursday, November 14, 2013 - 11:00am for 1 hour (actually 50 minutes)
Skyles 006
Chong-Qing Cheng – Nanjing University, China
Karim Lounici
In this talk, I shall sketch the study of the problem of Arnold diffusion from variational point of view. Arnold diffusion has been shown typical phenomenon in nearly integrable convex Hamiltonian systems with three degrees of freedom: $$ H(x,y)=h(y)+\epsilon P(x,y), \qquad x\in\mathbb{T}^3,\ y\in\mathbb{R}^3. $$ Under typical perturbation $\epsilon P$, the system admits ``connecting" orbit that passes through any two prescribed small balls in the same energy level $H^{-1}(E)$ provided $E$ is bigger than the minimum of the average action, namely, $E>\min\alpha$.