The purpose of this chapter is to develop the theory of a linear periodic RFDE that is analogous to the Floquet theory for ordinary differential equations. It is shown by example that a complete Floquet theory does not exist. However, it is possible to define characteristic multipliers and exploit the compactness of the solution operator to show that a Floquet representation exists on the generalized eigenspace of a characteristic multiplier. The decomposition of the space C by a characteristic multiplier is also applied to the variation-of-constants formula. The case of periodic delay equations with integer lags is considered in detail.
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