Qualitative Theory of Dynamical Systems

, Volume 18, Issue 3, pp 909–930 | Cite as

Singular Points of Polynomial Darboux Systems

  • Evgenii P. VolokitinEmail author


We study the singular points of the differential systems of the form \(\dot{x}= x+P(x,y), \ \dot{y}=y+Q(x,y)\) where P(xy) and Q(xy) are homogeneous polynomials of degree n.


Polynomial systems Singular points Poincaré equator Phase portraits 

Mathematics Subject Classification

34C05 34A34 34C14 



Funding was provided by Russian Foundation for Fundamental Investigations (Grant No. 18-01-00057) and Siberian Branch, Russian Academy of Sciences (Grant No. 0314-2016-0007).


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Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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