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arXiv · 2210.10245

A potential system with infinitely many critical periods

Jihua Wang
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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 $2\pi-$ 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)].

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Jihua Wang. 2022-10-19. A potential system with infinitely many critical periods. https://arxiv.org/abs/2210.10245

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