Estimates on the strength of exponential dichotomies and application to integral manifolds (Q1319937)

This paper is concerned with perturbations of linear differential equations having an exponential dichotomy. First of all the author presents a (slight) generalization of a known result due to D. Henry on linearly perturbed linear equations with an exponential dichotomy and bounded growth and decay. In this context two things are worth to be emphasized: First, the proof given in this paper is very explicit and so the mutual interdependence of the different dichotomy constants becomes transparent. And secondly, the proof of the theorem about a differential equation is based on an analysis of a corresponding difference equation. As an application of the above-mentioned dichotomy theorem the author derives a result on the persistence of integral manifolds for a certain class of nonlinear systems.