151. A computer-assisted proof of existence of a periodic solution
- Author
-
Tomoyuki Miyaji and Hisashi Okamoto
- Subjects
Conjecture ,General Mathematics ,Mathematical analysis ,Three-dimensional dynamical system ,Numerical verification ,Dynamical system ,37C27 ,Computer-assisted proof ,periodic orbit ,numerical verification ,Periodic orbits ,Heteroclinic orbit ,Uniqueness ,65G20 ,Poincaré map ,Mathematics - 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.
- Published
- 2014