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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
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 1480)

Abstract

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.

Keywords

Vector Field Inflection Point Bifurcation Theory Elliptic Integral Elliptic Case 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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