Averaging of time - periodic systems without a small parameter
Mickael Chekroun - Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris, France (email)
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
Keywords: Lie transforms, averaging method, equivalence, periodic solutions.
Received: January 2005; Revised: May 2005; Published: January 2006.
2011 Impact Factor.913