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.
@article{urn:eudml:doc:41255,
title = {Integrability of a linear center perturbed by a fourth degree homogeneous polynomial.},
journal = {Publicacions Matem\`atiques},
volume = {40},
year = {1996},
pages = {21-39},
mrnumber = {MR1397005},
zbl = {0851.34001},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41255}
}
Chavarriga, Javier; Giné, Jaume. Integrability of a linear center perturbed by a fourth degree homogeneous polynomial.. Publicacions Matemàtiques, Tome 40 (1996) pp. 21-39. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41255/