Abelian integrals in unfoldings of codimension 3 singular planar vector fields

Part I. The weakened 16-th Hilbert problem Part II. The saddle and elliptic cases Part III. The focus case
  • Freddy Dumortier
  • Robert Roussarie
  • Jorge Sotomayor
  • Henryk Żaładek
Part of the Lecture Notes in Mathematics book series (LNM, volume 1480)


In this work it is shown that, for small βi, the system \(\dot x\)=y, \(\dot y\)xx3+xy01y2x2y has at most two limit cycles when α≠(−1/8, ∞)∖{0} (Part II) and also when α<−1/8 (Part III). Part I contains an introduction to the problem, applications of Abelian integrals and some general results.


Vector Field Inflection Point Bifurcation Theory Elliptic Integral Elliptic Case 
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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Freddy Dumortier
  • Robert Roussarie
  • Jorge Sotomayor
  • Henryk Żaładek

There are no affiliations available

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