Revistes Catalanes amb Accés Obert (RACO)

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

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.

Text complet: PDF (English)