12:15 PM-1:15 PM
Room: Ballrooms I, II and III
Chair: Shui-Nee Chow, Georgia Institute of Technology, and University of Singapore
One of the most important problems in Hamiltonian dynamics concerns the stability of near-integrable systems. On one hand, KAM (Kolmogorov-Arnold-Moser) theory states that, in terms of measure, most orbits are stable. On the other hand, one believes that typical high dimensional Hamiltonian systems are topologically unstable, as conjectured by Arnold. The speaker will discuss some of the new methods and results concerning both stability and instability of the Hamiltonian dynamics. In particular, he will discuss the variational method and its applications to Arnold diffusion and various other problems concerning instability.
Zhihong Jeff Xia
Department of Mathematics