Advances in Difference Equations
Volume 2006 (2006), Article ID 57043, 19 pages
Invariant foliations and stability in critical cases
School of Mathematics, University of Minnesota, 206 Church Street SE, Minneapolis 55455, MN, USA
Received 29 January 2006; Revised 2 March 2006; Accepted 3 March 2006
Copyright © 2006 Christian Pötzsche. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We construct invariant foliations of the extended state space for nonautonomous semilinear dynamic equations on measure chains (time scales). These equations allow a specific parameter dependence which is the key to obtain perturbation results necessary for applications to an analytical discretization theory of ODEs. Using these invariant foliations we deduce a version of the Pliss reduction principle.