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arXiv · 1605.07775

Isochronous centers of polynomial Hamiltonian systems and a conjecture of Jarque and Villadelprat

Jacky Cresson·Jordy Palafox
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Abstract

We study the conjecture of Jarque and Villadelprat stating that every center of a planar polynomial Hamiltonian system of even degree is nonisochronous. This conjecture is proved for quadratic and quartic systems. Using the correction of a vector field to characterize isochronicity and explicit computations of this quantity for polynomial vector fields, wa are able to describe a very large class of nonisochronous Hamiltonian system of even degree of degree arbitrary large.

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Jacky Cresson, Jordy Palafox. 2016-05-25. Isochronous centers of polynomial Hamiltonian systems and a conjecture of Jarque and Villadelprat. https://arxiv.org/abs/1605.07775

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