On Lower Dimensional Tori in Hamiltonian Systems

Prof. Yingfei Yi

School of Mathematics
Georgia Institute of Technology

February 16, 2001

Abstract

The lecture will review some recent progress on KAM theory with emphasis on the persistence of lower dimensional tori in Hamiltonian systems. Some sharp persistence results on invariant tori of general type will be presented under non-resonance conditions of Melnikov type. Persistence results will also be presented for invariant tori of normal degeneracy and for non-integrable, hyperbolic invariant tori. Certain related infinite dimensional problems will be discussed with respect to the existence of quasi-periodic solutions in non-linear Schrödinger and wave equations.