Integrability of a linear center perturbed by a fourth degree homogeneous polynomial
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J. Chavarriga
J. Giné
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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Chavarriga, J.; and Giné, J. “Integrability of a linear center perturbed by a fourth degree homogeneous polynomial”. Publicacions Matemàtiques, vol.VOL 40, no. 1, pp. 21-39, https://raco.cat/index.php/PublicacionsMatematiques/article/view/37850.
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