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In this paper, a new rigorous numerical method to compute fundamental matrixsolutions of non-autonomous linear differential equations with periodiccoefficients is introduced. Decomposing the fundamental matrix solutions$\Phi(t)$ by their Floquet normal forms, that is as product of real periodicand exponential matrices $\Phi(t)=Q(t)e^{Rt}$, one solves simultaneously for$R$ and for the Fourier coefficients of $Q$ via a fixed point argument in asuitable Banach space of rapidly decaying coefficients. As an application, themethod is used to compute rigorously stable and unstable bundles of periodicorbits of vector fields. Examples are given in the context of the Lorenzequations and the $\zeta^3$-model.

Rigorous numerics in Floquet theory: computing stable and unstable bundles of periodic orbits