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

Autores: Jaume Giné Mesa , Javier Chavarriga Soriano
Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 41, Nº 2, 1997, págs. 335-356
Idioma: inglés
DOI: 10.5565/publmat_41297_02
Títulos paralelos:
- Integrabilidad de un centro lineal perturbado por un polinomio homogéneo de quinto grado
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Resumen
- In this work we study the integrability of two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fifth degree. We give a simple characterisation for the integrable cases in polar coordinates. Finally we formulate a conjecture about the independence of the two classes of parameters which appear on the system; if this conjecture is true the integrable cases found will be the only possible ones.