### Arnold diffusion in nearly integrable Hamiltonian systems

- Series
- School of Mathematics Colloquium
- Time
- Thursday, November 14, 2013 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skyles 006
- Speaker
- Chong-Qing Cheng – Nanjing University, China

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, $E>\min\alpha$.