Floquet theory

Summary

Floquet theory studies linear systems $x' = A(t)\, x$ whose coefficient matrix $A(t)$ is periodic in time. Its main result is that every fundamental matrix is a periodic matrix times a matrix exponential $e^{tB}$. So a periodic change of variables turns the system into one with constant coefficients. The behaviour of solutions, such as stability, is read off from the eigenvalues of the monodromy matrix, the Floquet multipliers. It applies to the Hill equation, to the stability of periodic orbits and to waves in periodic media. See the definition.