# 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

http://books.google.com/books?id=e1euiBF73yIC&dq=A+Second+Course+in+Differential+Equations+Paul+Waltman&printsec=frontcover&source=bl&ots=imup9X2PbZ&sig=g1__chkwNHxDDg-I7M48gjmjQL4&hl=en&ei=k5_dSu6KFM3l8QbEpJlh&sa=X&oi=book_result&ct=result&resnum=1&ved=0CA4Q6AEwAA#v=onepage&q=&f=false

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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