The 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...The 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.展开更多
基金Supported by Ministerio de Ciencia y Tecnología,Plan Nacional I+D+I co-financed with FEDER funds,in the frame of the pro jects MTM2010-20907-C02-02by Consejería de Educación y Ciencia de la Junta de Andalucía(Grant Nos.FQM-276 and P08-FQM-03770)
文摘The 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.
