zbMATH — the first resource for mathematics

A perturbation theorem for exponential dichotomies. (English) Zbl 0629.34058
It is well known that if the linear differential system \(x'=A(t)x\) has an exponential dichotomy, and B(t) is close to A(t) (in the sense of the sup-norm) then also the system \(y'=B(t)y\) has an exponential dichotomy. The author extends this classical result by weakening the assumption about closeness of A(t) and B(t). Applications to quasiperiodic equations are given.
Reviewer: A.Bacciotti

34D05 Asymptotic properties of solutions to ordinary differential equations
34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations
Full Text: DOI
[1] DOI: 10.1016/0022-0396(78)90057-8 · Zbl 0372.34027
[2] DOI: 10.1016/0022-0396(74)90067-9 · Zbl 0294.58008
[3] Sell, Topological Dynamics and Ordinary Differential Equations (1971)
[4] Coppel, Lecture Notes in Mathematics 629 (1978)
[5] Massera, Linear Differential Equations and Function Spaces (1966)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.