@article{10272/20904, year = {2019}, url = {http://hdl.handle.net/10272/20904}, abstract = {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.}, organization = {The first and second authors are partially supported by a MINECO/FEDER grant number MTM2014-56272-C2-2 and by the Consejer´ıa de Educaci ´on y Ciencia de la Junta de Andaluc´ıa (projects P12-FQM-1658, FQM-276). The third author is partially supported by a MINECO/FEDER grant number MTM2017- 84383-P and by an AGAUR (Generalitat de Catalunya) grant number 2014SGR 1204.}, publisher = {Elsevier}, title = {Integrability of planar nilpotent differential systems through the existence of an inverse integrating factor}, doi = {10.1016/j.cnsns.2018.09.018}, author = {Algaba Durán, Antonio and García García, Cristóbal and Giné, Jaume}, }