Integrability of a linear center perturbed by a fourth degree homogeneous polynomial

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1996Suggested citation
Chavarriga Soriano, Javier;
Giné, Jaume;
.
(1996)
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Integrability of a linear center perturbed by a fourth degree homogeneous polynomial.
Publicacions matemàtiques, 1996, vol. 40, núm. 1, p. 21-39.
https://doi.org/10.5565/PUBLMAT_40196_03.
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In this work we study the integrability of a two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fourth degree. We give sufficient conditions for integrability in polar coordinates. Finally we establish a conjecture about the independence of the two classes of parameters which appear in the system; if this conjecture is true the integrable cases found will be the only possible ones.
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Publicacions matemàtiques, 1996, vol. 40, núm. 1, p. 21-39European research projects
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