zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
On the reducibility of linear differential equations with quasiperiodic coefficients. (English) Zbl 0761.34026
We say that a matrix Q(t) is a quasiperiodic matrix of time with basic frequencies ω 1 ,,ω r if Q(t)=F(ω 1 t,,ω r t), where F=F(v 1 ,,v r ) is 2π periodic in all its arguments. The author considers the system (1) x ' =(A+εQ(t))x, where A is a constant matrix and Q(t) is a quasiperiodic analytic matrix with r basic frequencies. Suppose A has different eigenvalues (including the purely imaginary case) and the set formed by the eigenvalues of A and the basic frequencies of Q(t) satisfies a nonresonant condition. It is proved under a nondegeneracy condition that there exists a Cantorian set 𝒮(0,ε 0 ) (ε 0 >0) with positive Lebesgue measure such that for ε𝒮 (1) is reducible (i.e. there exists a nonsingular quasiperiodic matrix P(t) such that P(t), P -1 (t) and P ' (t) are bounded on R and the change of variables x=P(t)y transforms (1) to y ' =By with a constant matrix B).

34C20Transformation and reduction of ODE and systems, normal forms
34A30Linear ODE and systems, general
34C27Almost and pseudo-almost periodic solutions of ODE