# American Institute of Mathematical Sciences

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

 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].
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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