Linear Ordinary Differential Equations with Quasiperiodic Coefficients

Abstract

In this section we wish to study the general form of the solution matrix Q(t) of the differential equation

$$ \dot Q\left( t \right) = M\left( t \right)Q\left( t \right) $$

((3.1.1))

where M is a complex-valued m × m matrix which can be expressed as a Fourier series of the form

$$ M\left( t \right) = \sum\limits_{n1,n2, \ldots ,nN} {M_{n1,n2, \ldots ,nN} \exp } \left( {{\text{i}}\omega _1 n_1 t + {\text{i}}\omega _N n_N t} \right). $$

((3.1.2))

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