A potential system with infinitely many critical periods
Classical Analysis and ODEs
2023-10-09 v2
Abstract
In this paper, we propose an analytical non-polynomial potential system which has infinitely many critical periodic orbits in phase plane. By showing the existence of infinitely many periodic solutions, the proof bases on variational methods and the properties of Bessel function. The result provides an affirmative example to Dumortier's conjecture [Nonlinear Anal. 20(1993)].
Cite
@article{arxiv.2210.10245,
title = {A potential system with infinitely many critical periods},
author = {Jihua Wang},
journal= {arXiv preprint arXiv:2210.10245},
year = {2023}
}
Comments
10 pages