A computer-assisted proof of existence of a periodic solution

A computer-assisted proof of existence of a periodic solution

We consider a three-dimensional dynamical system proposed in \textit{Physica D}, \textbf{164}, (2002), 168-186. It is a conservative system and is unusual in that most of the solutions are unbounded. The paper presented a conjecture that an unstable periodic orbit determines directions of unbounded...

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Veröffentlicht in:Proceedings of the Japan Academy. Series A. Mathematical sciences 2014-12, Vol.90 (10), p.139-144
Hauptverfasser: Miyaji, Tomoyuki, Okamoto, Hisashi
Format: Artikel
Sprache:eng
Schlagworte:
37C27
65G20
Computational mathematics
Differential equations
Dynamical systems
Dynamics
Helical
Mathematical models
numerical verification
Orbits
periodic orbit
Series (mathematics)
Three dimensional
Three-dimensional dynamical system
Uniqueness
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Zusammenfassung:We consider a three-dimensional dynamical system proposed in \textit{Physica D}, \textbf{164}, (2002), 168-186. It is a conservative system and is unusual in that most of the solutions are unbounded. The paper presented a conjecture that an unstable periodic orbit determines directions of unbounded orbits of helical form. In the present paper we prove existence and local uniqueness of the conjectured periodic orbit by a method of numerical verification.
ISSN:0386-2194
DOI:10.3792/pjaa.90.139