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August  2010, 27(3): 963-980. doi: 10.3934/dcds.2010.27.963

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

Magdalena Caubergh 1, , Freddy Dumortier 2, and  Stijn Luca 3,

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  August 2009 Revised  November 2009 Published  March 2010

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; 34D1.
Citation: Magdalena Caubergh, Freddy Dumortier, Stijn Luca. Cyclicity of unbounded semi-hyperbolic 2-saddle cycles in polynomial Lienard systems. Discrete and Continuous Dynamical Systems, 2010, 27 (3) : 963-980. doi: 10.3934/dcds.2010.27.963
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