Speaker : Professor H. Scott Dumas (University of Cincinnati & University of New Mexico)
Title : A Multiphase Averaging Method for Quasiperiodic Systems of ODEs
Time : 2020-01-06 (Mon) 15:00 - 16:00
Place : Seminar Room 722, Institute of Mathematics (NTU Campus)
Abstract: I'll present a simple, specialized averaging method for systems of ordinary differential equations with fast variables evolving quasiperiodically. This includes results for both nonresonant and resonant normal forms, and results on adiabatic invariance for systems with vanishing average. In this method, nonresonance conditions on the frequencies are weak and easily verified, and they give precise meaning to the notion that "resonances above a certain order may be ignored." Moreover, the normal forms have nice dependence on the frequencies, and the proofs are especially simple, involving no coordinate transformations and instead using a new generalized form of the "Besjes inequality."