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July  2005, 13(4): 901-920. doi: 10.3934/dcds.2005.13.901

Topological method for rigorously computing periodic orbits using Fourier modes

Anthony W. Baker 1, , Michael Dellnitz 1, and  Oliver Junge 1,

1. 

Institute for Mathematics, University of Paderborn, D-33095 Paderborn, Germany, Germany, Germany

Received  December 2004 Revised  July 2005 Published  August 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 [2].
Keywords: periodic orbit, set oriented methods, Dynamical system, computer assisted proof..
Mathematics Subject Classification: Primary: 34L30, 37B30, 37M99; Secondary: 37C25, 65P9.
Citation: Anthony W. Baker, Michael Dellnitz, Oliver Junge. Topological method for rigorously computing periodic orbits using Fourier modes. Discrete and Continuous Dynamical Systems, 2005, 13 (4) : 901-920. doi: 10.3934/dcds.2005.13.901
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