Abelian integrals and global hopf bifurcations

  • J. A. Sanders
  • R. Cushman
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1125)


We give a detailed and simplified proof of a theorem of Yu. S. Il'yashenko which concerns the uniqueness of certain limit cycles. A slightly extended version of this theorem is then applied to a global Hopf bifurcation problem treated by Keener.


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Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • J. A. Sanders
    • 1
  • R. Cushman
    • 2
  1. 1.Department of Mathematics and Computer ScienceVrije UniversiteitAmsterdamthe Netherlands
  2. 2.Mathematics InstituteRijksuniversiteit UtrechtUtrechtthe Netherlands

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