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A dynamical systems result on asymptotic integration of linear differential systems. (English) Zbl 1037.34042
The author studies, under a dynamical systems point of view, the asymptotic integration of linear differential systems of the form $x^{\prime }=[\Lambda (t)+R(t)]x$, where $\Lambda$ is diagonal and $R\in L^{p}[t_{0},\infty )$ for $p\in \lbrack 1,2]$. By using the theory of linear skew-product flows, the paper presents a dichotomy condition in terms of the spectrum over the omega-limit set $w_{\Lambda }$. The theory is illustrated by two examples that are not covered by the Hartman-Winter theorem.

##### MSC:
 34D09 Dichotomy, trichotomy 34A30 Linear ODE and systems, general 34L05 General spectral theory for OD operators
##### Keywords:
linear systems; asymptotic integration; spectral theory
Full Text:
##### References:
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