A potential system with infinitely many critical periods
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 2π- 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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