# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
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 ${x}^{\text{'}}=\left[{\Lambda }\left(t\right)+R\left(t\right)\right]x$, where ${\Lambda }$ is diagonal and $R\in {L}^{p}\left[{t}_{0},\infty \right)$ for $p\in \left[1,2\right]$. 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