Averaging of time-periodic systems without a small parameter

Details Averaging of time-periodic systems without a small parameter Averaging of time-periodic systems without a small parameter

2010-06-14

arxiv.org/abs/1006.2789v1

Discrete and Continuous Dynamical Systems, Ser. A, {\bf 14}(4), (2006) 753-782

Mathematics

Dynamical Systems

This version contains a proof of Lemma 6.1 from the published version

Scientific paper

In this article, we present a new approach to averaging in non-Hamiltonian systems with periodic forcing. The results here do not depend on the existence of a small parameter. In fact, we show that our averaging method fits into an appropriate nonlinear equivalence problem, and that this problem can be solved formally by using the Lie transform framework to linearize it. According to this approach, we derive formal coordinate transformations associated with both first-order and higher-order averaging, which result in more manageable formulae than the classical ones. Using these transformations, it is possible to correct the solution of an averaged system by recovering the oscillatory components of the original non-averaged system. In this framework, the inverse transformations are also defined explicitly by formal series; they allow the estimation of appropriate initial data for each higher-order averaged system, respecting the equivalence relation. Finally, we show how these methods can be used for identifying and computing periodic solutions for a very large class of nonlinear systems with time-periodic forcing. We test the validity of our approach by analyzing both the first-order and the second-order averaged system for a problem in atmospheric chemistry.

Affiliated with

Also associated with

No associations

Rating

Averaging of time-periodic systems without a small parameter does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Averaging of time-periodic systems without a small parameter, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Averaging of time-periodic systems without a small parameter will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-422988