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Estimates on the strength of exponential dichotomies and application to integral manifolds. (English) Zbl 0811.34007
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.

MSC:
34A30 Linear ordinary differential equations and systems, general
34D10 Perturbations of ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
34C30 Manifolds of solutions of ODE (MSC2000)
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