Local phase portraits through the Newton diagram of a vector field

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• 作者：Antonio Algaba ; Isabel Checa ; Cristóbal García…
• 关键词：Monodromy ; separatrices ; phase portraits ; quasi ; homogeneous vector field ; 34C05 ; 34M35
• 刊名：Acta Mathematica Sinica
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：31
• 期：6
• 页码：1015-1034
• 全文大小：393 KB
• 参考文献：[1]Algaba, A., García, C., Reyes, M.: A new algorithm for determining the monodromy of a planar differential system. Appl. Math. Comput., 237, 419-29 (2014)View Article MathSciNet
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  [6]Artés, 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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  [12]Zhang, Z. F., Ding, T. R., Huang, W. Z., et al.: Qualitative Theory of Differential Equations, Trans. Math. Monographs, 101, Amer. Math. Soc., Providence, RI, 1992
  
• 作者单位：Antonio Algaba (1)
  Isabel Checa (1)
  Cristóbal García (1)
  Manuel Reyes (1)
  
  1. Department of Mathematics, Faculty of Experimental Sciences, Avda. Tres de Marzo s/n, 21071, Huelva, Spain
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Chinese Library of Science
  
• 出版者：Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society, co-published
• ISSN：1439-7617

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.