EVENT DETAILS AND ABSTRACT

Title: Speed of Arnold diffusion for analytic Hamiltonian systems
Speaker: Ke Zhang
Speaker Info: University of Maryland
Brief Description:
Special Note:
Abstract:

For a close-to-integrable Hamiltonian system with more than 2 degree of freedom, the existence of orbits whose action varible makes $O(1)$ change is often refered to as Arnold diffusion. For quasi-convex analytic Hamiltonians that is $\epsilon-$close to integrable, Nekhoroshev theory predicts a stability time of $\exp(C\epsilon^{\frac{1}{2n}})$, or $\exp(C\epsilon^{-\frac{1}{2(n-m)}})$ if the initial condition is is close to $m-$resonances. This gives a upper bound on the speed of Arnold diffusion. We show that this upper bound is optimal by giving an example for which diffusion happens in $\exp(C\epsilon^{-\frac{1}{2(n-2)}})$ time, while the orbit is close to a double resonance.