Floquet multiplier

Floquet theory is a branch of the theory of ordinary differential equations relating to the class of solutions to periodic linear differential equations of the form

with ${\displaystyle \displaystyle A(t)}$ a piecewise continuous periodic function with period ${\displaystyle T}$ and defines the state of the stability of solutions.

The main theorem of Floquet theory, Floquet's theorem, due to Gaston Floquet (1883), gives a canonical form for each fundamental matrix solution of this common linear system. It gives a coordinate change ${\displaystyle \displaystyle y=Q^{-1}(t)x}$ with ${\displaystyle \displaystyle Q(t+2T)=Q(t)}$ that transforms the periodic system to a traditional linear system with constant, real coefficients.

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