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Local Phase Portraits through the Newton Diagram of a Vector Field

Local Phase Portraits through the Newton Diagram of a Vector Field
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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.
作者 Antonio ALGABA Isabel CHECA Cristóbal GARCIA Manuel REYES
机构地区 Department of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 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)
关键词 MONODROMY separatrices phase portraits quasi-homogeneous vector field Monodromy, separatrices, phase portraits, quasi-homogeneous vector field
分类号 O157.5 [理学—基础数学]
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参考文献12

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  • 6Art,s, J. C., Dumortier, F., Herssens, C., et al.: Computer program P4 to study phase portraits planar ploynomial differential equations, http://mat.uab.es/-artes/p4/p4.htm.
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  • 8Brunella, M., Miari, M.: Topological equivalence of a plane vector field with its principal part defined through Newton polyhedra. J. Differential Equations, 85(2), 338 366 (1990).
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Acta Mathematica Sinica,English Series
2015年 第6期

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