Topological method for rigorously computing periodic orbits using Fourier modes | Zendy

Anthony W. Baker | Zendy; Michael Dellnitz | Zendy; Oliver Junge | Zendy

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Topological method for rigorously computing periodic orbits using Fourier modes

Author(s) -

Anthony W. Baker,

Michael Dellnitz,

Oliver Junge

Publication year - 2005

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2005.13.901

Subject(s) - periodic orbits , ordinary differential equation , computation , dynamical systems theory , invariant (physics) , differential equation , set (abstract data type) , orbit (dynamics) , topology (electrical circuits) , fourier transform , mathematics , mathematical analysis , computer science , physics , algorithm , mathematical physics , quantum mechanics , combinatorics , aerospace engineering , engineering , programming language

We present a technique for the rigorous computation of periodic orbits in certain ordinary dierential 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 dierential equation introduced in (

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