A computer-assisted proof of existence of a periodic solution

作者：Miyaji Tomoyuki^*; Okamoto Hisashi

来源：Proceedings of the Japan Academy Series A-Mathematical Sciences, 2014, 90(10): 139-144.

DOI：10.3792/pjaa.90.139

• Three-dimensional dynamical system
• periodic orbit
• numerical verification

We consider a three-dimensional dynamical system proposed in Physica D, 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.

• 出版日期2014-12