The determinantal method for Hill systems

where G ∈ L∞(IR, IRn×n) is a matrix valued function with G(x+1) = G(x) for almost every x ∈ IR. Systems of this type appear, for instance, in the theory of vibrations or in hydrodynamics. In the typical case where the function G depends on some set of parameters, one is not really interested in the solution of (1) but in the values of the parameters for which this equation is stable. Let Y : IR→ IR2n×2n be the fundamental solution of (1), i.e. the solution of the initial value problem