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

Magdalena Caubergh; Freddy Dumortier; Stijn Luca

doi:10.3934/dcds.2010.27.963

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2010, Volume 27, Issue 3: 963-980. Doi: 10.3934/dcds.2010.27.963

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

1.
Departament de Matemàtiques, Edifici C, Universitat Autònoma de Barcelona, 08193 Cerdanyola de Vallès, Barcelona
2.
Universiteit Hasselt, Campus Diepenbeek, Agoralaan–gebouw D, 3590 Diepenbeek
3.
Universiteit Hasselt, Campus Diepenbeek, Agoralaan - Gebouw D, B-3590 Diepenbeek

Received: July 31, 2009

Revised: October 31, 2009

Published: August 2010

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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.

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

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