Baker, A.; Dellnitz, M.; Junge, O.:
A topological method for rigorously computing periodic orbits using Fourier modes
Discrete and Continuous Dynamical Systems, 13(4): 901-920, 2005.

We present a technique for the rigorous computation of periodic orbits in certain ordinary differential equations. The method combines set oriented numerical techniques for the computation of invariant sets in dynamical systems with topological index arguments. It not only allows for the proof of existence of periodic orbits but also for a precise (and rigorous) approximation of these. As an example we compute a periodic orbit for a differential equation introduced in \cite{MR87f:58094}.

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