@article{10272/20906, year = {2016}, url = {http://hdl.handle.net/10272/20906}, abstract = {This paper is devoted to the classification of analytic integrable cases of two families of degenerate planar vector fields with a monodromic singular point at the origin. This study falls in the still open degenerate center problem. This classification can be done using the formal normal form theory and knowing a suitable normal form of any differential systems associated to each family.}, abstract = {This paper is devoted to the classification of analytic integrable cases of two families of degenerate planar vector fields with a monodromic singular point at the origin. This study falls in the still open degenerate center problem. This classification can be done using the formal normal form theory and knowing a suitable normal form of any differential systems associated to each family.}, organization = {The authors are grateful to the referees for their valuable remarks which helped to improve the manuscript. The first and second authors are supported by a MINECO/FEDER grant number MTM2010-20907-C02-02 and by the Consejería de Educación y Ciencia de la Junta de Andalucía (projects P12-FQM-1658; TIC-130 and FQM-276). The third author is partially supported by a MINECO/FEDER grant number MTM2011-22877 and by an AGAUR (Generalitat de Catalunya) grant number 2014SGR 1204.}, publisher = {Springer}, title = {Analytic Integrability of Some Examples of Degenerate Planar Vector Fields}, doi = {10.1007/s10440-014-0001-2}, author = {Algaba Durán, Antonio and García García, Cristóbal and Giné, Jaume}, }