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2005, Volume 13, Issue 4: 901-920. Doi: 10.3934/dcds.2005.13.901
This issue Previous Article Instability of travelling wave profiles for the Lax-Friedrichs scheme Next Article Comparison of quarter-plane and two-point boundary value problems: the BBM-equation

Topological method for rigorously computing periodic orbits using Fourier modes

  • 1.

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

Received:  November 30, 2004
Revised:  June 30, 2005
Published:  June 2005
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    Abstract
  • 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].
    Mathematics Subject Classification: Primary: 34L30, 37B30, 37M99; Secondary: 37C25, 65P99.

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