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.
@article{urn:eudml:doc:41322,
title = {Integrability of a linear center perturbed by a fifth degree homogeneous polynomial.},
journal = {Publicacions Matem\`atiques},
volume = {41},
year = {1997},
pages = {335-356},
mrnumber = {MR1485487},
zbl = {0897.34030},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41322}
}
Chavarriga, Javier; Giné, Jaume. Integrability of a linear center perturbed by a fifth degree homogeneous polynomial.. Publicacions Matemàtiques, Tome 41 (1997) pp. 335-356. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41322/