Isochronous centers of polynomial Hamiltonian systems and a conjecture of Jarque and Villadelprat
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 has already been proved for quadratic and quartic systems. Using the correction of a vector field to characterize isochronicity and...
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| Veröffentlicht in: | Journal of Differential Equations 2019-04, Vol.266 (9), p.5713-5747 |
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| container_title | Journal of Differential Equations |
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| creator | Cresson, Jacky Palafox, Jordy |
| description | 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 has already been 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, we are able to describe a very large class of nonisochronous Hamiltonian systems of even arbitrarily large degree. |
| doi_str_mv | 10.1016/j.jde.2018.10.032 |
| format | Article |
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| title | Isochronous centers of polynomial Hamiltonian systems and a conjecture of Jarque and Villadelprat |
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