Slow and Fast Variables in Nonautonomous Difference Equations
by
Christian Poetzsche
Department of Mathematics, University of Augsburg, D-86135 Augsburg, Germany

We present an existence and smoothness result for center-like invariant manifolds of nonautonomous difference equations with slow and fast state-space variables. This result can be seen as a first step to obtain Fenichel's geometric theory in the setting of difference equations. Here, our basic tools are a flexible robustness theorem for exponential dichotomies under slowly varying coefficients, and an abstract integral manifold theorem.

2000 Mathematics Subject Classification. 39A11, 34K19, 34E15

Keywords. Invariant manifolds, singular perturbations, difference equations

Date received: February 21, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cakr-41.