Cyclicity of unbounded semi-hyperbolic 2-saddle cycles in polynomial Lienard systems

Pages: 963 - 980, Volume 27, Issue 3, July 2010

doi:10.3934/dcds.2010.27.963       Abstract        Full Text (850.1K)       Related Articles

Magdalena Caubergh - Departament de Matemàtiques, Edifici C, Universitat Autònoma de Barcelona, 08193 Cerdanyola de Vallès, Barcelona, Spain (email)
Freddy Dumortier - Universiteit Hasselt, Campus Diepenbeek, Agoralaan–gebouw D, 3590 Diepenbeek, Belgium (email)
Stijn Luca - Universiteit Hasselt, Campus Diepenbeek, Agoralaan - Gebouw D, B-3590 Diepenbeek, Belgium (email)

Abstract: The paper deals with the cyclicity of unbounded semi-hyperbolic 2-saddle cycles in polynomial Liénard systems of type $(m,n)$ with $m<2n+1$, $m$ and $n$ odd. We generalize the results in [1] (case $m=1$), providing a substantially simpler and more transparant proof than the one used in [1].

Keywords:  Liénard equation; limit cycle; heteroclinic connection; cyclicity.
Mathematics Subject Classification:  34C07; 34C37; 34D10.

Received: August 2009;      Revised: November 2009;      Published: March 2010.