Algebraic integrability of nilpotent planar vector fields. (April 2021) - Algaba, A.
Abstract: We characterize, using normal forms of quasi-homogeneous expansions, the analytic vector fields at nilpotent singular point having an algebraic first integral over the ring C [ [ x, y ] ] . As a consequence, we provide a link between the algebraic integrability problem and the existence of a formal inverse integrating factor which is null at the singular point.