On the reducibility of linear differential equations with quasiperiodic coefficients

https://doi.org/10.1016/0022-0396(92)90107-XGet rights and content
Under an Elsevier user license
open archive

Abstract

The system ẋ = (A + εQ(t))x in Rd is considered, where A is a constant matrix and Q a quasiperiodic analytic matrix with r basic frequencies. The eigenvalues of A are arbitrary including the purely imaginary case. Suppose that the set formed by the eigenvalues of A and the basic frequencies of Q satisfies a nonresonant condition. Then there is a positive measure cantorian set E such that for ε ϵ E the system is reducible to constant coefficients by means of a quasiperiodic change of variables, provided a nondegeneracy condition holds. This condition prevents locking at resonance.

Cited by (0)