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Zbl 0629.34058
Palmer, Kenneth J.
A perturbation theorem for exponential dichotomies. (English)
[J] Proc. R. Soc. Edinb., Sect. A 106, 25-37 (1987). ISSN 0308-2105; ISSN 1473-7124/e

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.
[A.Bacciotti]

MSC 2000:: *34D05 Asymptotic stability of ODE
34C27 Almost periodic solutions of ODE

Keywords: exponential dichotomy; quasiperiodic equations

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