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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

##### MSC:
 34D05 Asymptotic properties of solutions to ordinary differential equations 34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations
##### Keywords:
exponential dichotomy; quasiperiodic equations
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##### References:
 [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)
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