A new approach to highorder averaging
Abstract
We present a new approach to perform highorder averaging in oscillatory periodic or quasiperiodic dynamical systems. The averaged system is expressed in terms of (i) scalar coefficients that are universal, i.e. independent of the system under consideration and (ii) basis functions that may be written in an explicit, systematic way in terms of the derivatives of the Fourier coefficients of the vector field being averaged. The coefficients may be recursively computed in a simple fashion. This approach may be used to obtain exponentially small error estimates, as those first derived by Neishtadt for the periodic case and Simó in the quasiperiodic scenario.
 Publication:

Numerical Analysis and Applied Mathematics ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics
 Pub Date:
 September 2012
 DOI:
 10.1063/1.4756057
 Bibcode:
 2012AIPC.1479...42C
 Keywords:

 estimation theory;
 Fourier analysis;
 Lie algebras;
 Lie groups;
 02.10.Ud;
 02.20.Sv;
 02.30.Hq;
 02.30.Nw;
 Linear algebra;
 Lie algebras of Lie groups;
 Ordinary differential equations;
 Fourier analysis