Algaba Durán, AntonioCheca Camacho, IsabelGarcía García, CristóbalReyes Columé, Manuel2025-05-082025-05-082015-06Algaba, A., Checa, I., García, C., & Reyes, M. (2015). Local phase portraits through the Newton diagram of a vector field. Acta Mathematica Sinica, English Series, 31(6), 1015–1034. https://doi.org/10.1007/s10114-015-3663-410.1007/s10114-015-3663-41439-85161439-7617 (electrónico)https://hdl.handle.net/10272/25454The Newton diagram and, in particular, the lowest-degree quasi-homogeneous terms of an analytic planar vector field allow us to determine the existence of characteristic orbits and separatrices of an isolated singular point. We give an easy algorithm for obtaining the local phase portrait near the origin of a bi-dimensional differential system and we provide several examples.engAtribución-SinDerivadas 3.0 Españahttp://creativecommons.org/licenses/by-nd/3.0/es/Ecuaciones diferencialesDegenerate vector fieldsPhase portraitsMonodromy of vector fieldsMonodromySeparatricesQuasi-homogeneous vector fieldjournal articleopen access1206.02 Ecuaciones Diferenciales