Local Phase Portraits through the Newton Diagram of a Vector Field  

作　　者：Antonio ALGABA Isabel CHECA Cristóbal GARCIA Manuel REYES 

机构地区：[1]Department of Mathematics, Faculty of Experimental Sciences

出　　处：《Acta Mathematica Sinica,English Series》2015年第6期1015-1034,共20页数学学报（英文版）

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-C02-02;by Consejería de Educación y Ciencia de la Junta de Andalucía(Grant Nos.FQM-276 and P08-FQM-03770)

摘　　要：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.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.

关 键 词：MONODROMY separatrices phase portraits quasi-homogeneous vector field 

分 类 号：O157.5[理学—数学]