English

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 2π2\pi- 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)].

Keywords

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

R2 v1 2026-06-28T03:57:44.096Z