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On linear differential equations with almost periodic coefficients and the property that the unit sphere is invariant. (English) Zbl 0555.34038

Equadiff 82, Proc. int. Conf., Würzburg 1982, Lect. Notes Math. 1017, 364-368 (1983).
[For the entire collection see Zbl 0511.00014.]
Solutions x(t) of \(x'=A(t)x\) need not be quasiperiodic [abbreviated to QP] even though the \(n\times n\) matrix A is QP and skew Hermitian. However the set of QP matrices for which the solutions are also QP may be dense in the set of all QP matrices. In particular, this is shown to be so in the case that both A and x have no more than \(r+1\) fundamental frequencies, \(r=1\) or 2, \(n\geq 2\) in the complex case, \(n\geq 3\) in the real case.
Reviewer: C.Coleman

MSC:

34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations
34A30 Linear ordinary differential equations and systems

Citations:

Zbl 0511.00014