Integrability of planar nilpotent differential systems through the existence of an inverse integrating factor

摘要

In this work is characterized the analytic integrability problem around a nilpotent singularity for differential systems in the plane under generic conditions. The analytic integrability problem is characterized via the existence of a formal inverse integrating factor. The relation between the analytic integrability and the existence of an algebraic inverse integrating factor is also given. (C) 2018 Elsevier B.V. All rights reserved.