Dynamical Systems Seminar

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

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
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