Algaba Durán, AntonioGarcía García, Cristóbal, MatemáticoReyes Columé, Manuel2025-04-112025-04-112020-030022-247X1096-0813 (electrónico)https://hdl.handle.net/10272/25370We characterize the analytic planar vector fields orbitally equivalent to its quasi-homogeneous leader term, by means the existence of a class of inverse integrating factors. Such a class of inverse integrating factors is determined by providing a normal form of two-dimensional scalar functions. This fact allows us to give some relevant criteria on t-linearization, analytical integrability and characterization of the centers for several families of planar vector fields. We study the systems whose leader term is quadratic or cubic and we analyze also a class of nilpotent systemsengAtribución-SinDerivadas 3.0 Españahttp://creativecommons.org/licenses/by-nd/3.0/es/Linearization of vector fieldsDegenerate vector fieldsQuadratic and cubic systemsjournal article10.1016/j.jmaa.2019.123635open access12 Matemáticas