A computer-assisted proof of existence of a periodic solution

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Tomoyuki Miyaji¹  Hisashi Okamoto² 

[1] Organization for the Strategic Coordination of Research and Intellectual Properties, Meiji University;Research Institute for Mathematical Sciences, Kyoto University

关键词: Three-dimensional dynamical system;    periodic orbit;    numerical verification.;   

DOI  :  10.3792/pjaa.90.139

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

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.

【 授权许可】

Unknown