## EVENT DETAILS AND ABSTRACT

**Dynamical Systems Seminar**
**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.

**Date:** Tuesday, September 29, 2009

**Time:** 3:00pm

**Where:** Lunt 105

**Contact Person:** Prof. Pat Hooper

**Contact email:** wphooper@math.northwestern.edu

**Contact Phone:** 847-491-2853

Copyright © 1997-2024
Department of Mathematics, Northwestern University.