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Floquet Multipliers

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The text we are using is "A Second Course in Elementary Differential equations" by Paul Waltman. This section begins on page 77. Here is the link to the book


Let p(t) be a continuous function of period omega. consider the system x'=Ax, where A=[0,1;p(t),0].

(a.) Let Phi(t)be a fundamental matrix such that Phi(0)=I, where I is the 2X2 identity matrix. Show that the determinant of the fundamental matrix is one for all t.

(b.) Show that the Floquet Multipliers are the roots of f^2-nf+1=0, where n is the trace of the fundamental matrix.

(c.) If n=2, show that the differential equation has a solution of period omega.

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Solution Summary

Floquet Multipliers are expressed for periodic coefficients.

Solution Preview

Consider the equation , where and is a periodical function with period .
(a) From the condition, is a fundamental matrix with . Let be the determinant of , then we have the formula

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