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Topological method for rigorously computing periodic orbits using Fourier modes
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 [2].