Advances in Difference Equations
Volume 2006 (2006), Article ID 57043, 19 pages
doi:10.1155/ADE/2006/57043

Invariant foliations and stability in critical cases

Abstract

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.