Past Event: Oden Institute Seminar

Multi time scale averaging to all orders: Rigorous theory and Computational Applications ****in POB 4.304****

Avraham Soffer, Rutger's University

Abstract

Dynamical systems with Hamiltonians changing in time can be studied by averaging over the fast oscillations, or by adiabatic approximation in the case of slowly changing dynamics. In both cases, the averaged dynamics is useful up to finite time only, given by the inverse of the small parameter. I will describe a recently developed new approach, in which the averaging can be done on larger and larger time scales, in a way that gives rigorously controlled errors to all orders in the small parameter, and to arbitrary large time intervals. As such, it is a new way to derive and understand Nekhoroshev type theorems. I then present applications: new proof of adiabatic theorems and scattering for time dependent potentials. Then I will present numerical scheme for dispersive wave equations with controlled errors to very large time scales (10^3-10^7).