Proceedings of the Japan Academy, Series A, Mathematical Sciences

A computer-assisted proof of existence of a periodic solution

Tomoyuki Miyaji and Hisashi Okamoto

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Abstract

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.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 90, Number 10 (2014), 139-144.

Dates
First available in Project Euclid: 4 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.pja/1417707834

Digital Object Identifier
doi:10.3792/pjaa.90.139

Mathematical Reviews number (MathSciNet)
MR3290437

Zentralblatt MATH identifier
1348.37037

Subjects
Primary: 37C27: Periodic orbits of vector fields and flows 65G20: Algorithms with automatic result verification

Keywords
Three-dimensional dynamical system periodic orbit numerical verification

Citation

Miyaji, Tomoyuki; Okamoto, Hisashi. A computer-assisted proof of existence of a periodic solution. Proc. Japan Acad. Ser. A Math. Sci. 90 (2014), no. 10, 139--144. doi:10.3792/pjaa.90.139. https://projecteuclid.org/euclid.pja/1417707834


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