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
Famous quotes containing the word theorem:
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (19131960)
Related Phrases
Related Words