DCDS
Topological method for rigorously computing periodic orbits using Fourier modes
Anthony W. Baker Michael Dellnitz Oliver Junge
Discrete & Continuous Dynamical Systems - A 2005, 13(4): 901-920 doi: 10.3934/dcds.2005.13.901
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].
keywords: periodic orbit set oriented methods Dynamical system computer assisted proof.

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