Analytic integrability and characterization of centers for generalized nilpotent singular points

摘要

A method which provides necessary conditions for obtaining a local analytic integral in a neighborhood of a generalized nilpotent singular point is developed. This method is applied to several classes of generalized nilpotent systems. We obtain sufficient conditions for each case finding an inverse integrating factor or a local first integral defined at the origin. We study which ones of the found cases possess a center at the origin.