Floquet Theory - Floquet's Theorem

Floquet's Theorem

Let be a linear first order differential equation, where is a column vector of length and an periodic matrix with period (that is for all real values of ). Let be a fundamental matrix solution of this differential equation. Then, for all ,

Here

is known as the monodromy matrix. In addition, for each matrix (possibly complex) such that

there is a periodic (period ) matrix function such that

Also, there is a real matrix and a real periodic (period-) matrix function such that

In the above, and are matrices.

Read more about this topic:  Floquet Theory

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