Estimates on the strength of exponential dichotomies and application to integral manifolds.

*(English)*Zbl 0811.34007This 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.

Reviewer: B.Aulbach (Augsburg)

##### 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) |