Floquet's Theorem

Let  be a real or complex piecewise-continuous function defined for all values of the real variable  and that is periodic with minimum period  so that

(1)

Then the differential equation

(2)

has two continuously differentiable solutions  and , and the characteristic equation is

(3)

with eigenvalues  and . Then Floquet's theorem states that if the roots  and  are different from each other, then (2) has two linearly independent solutions

			(4)
			(5)

where  and  are periodic with period  (Magnus and Winkler 1979, p. 4).

REFERENCES:

Magnus, W. and Winkler, S. "Floquet's Theorem." §1.2 in Hill's Equation. New York: Dover, pp. 3-8, 1979.