Analytic integrability and characterization of centers for generalized nilpotent singular points. (Q1421285)

The author studies the existence of local analytic first integrals for a generalized nilpotent singular point. He develops a method which provides necessary conditions for obtaining a local analytic integral in a neighborhood of a generalized nilpotent singular point. He considers several classes of generalized nilpotent systems and obtains sufficient conditions guaranteeing an inverse integrating fact or a local first integral near the origin. He studies under which conditions there is a center at the origin.