Analytic integrability of a class of nilpotent cubic systems
In this paper, we study a family of nilpotent cubic systems having an isolated singular point at the origin and we give a characterization of those that accept a certain type of analytic first integrals. For these systems, we also give a characterization of the singular point at the origin; in particular, we see that the origin is never a center. (C) 2002 IMACS. Published by Elsevier Science B.V. All rights reserved.
analytic integrability nilpotent cubic systems center problem