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August  2009, 24(3): 699-729. doi: 10.3934/dcds.2009.24.699

Quadratic perturbations of a class of quadratic reversible systems with two centers

B. Coll 1, , Chengzhi Li 2, and  Rafel Prohens 3,

1. 

Dept. de Matemàtiques i Informàtica, Universitat de les Illes Balears, Escola Politècnica Superior, 07122-Palma de Mallorca
2. 

School of Mathematical Sciences and LMAM, Peking University, Beijing, 100871, China
3. 

Dep. de Matemàtiques i Informàtica. Univ. de Illes Balears, 07122-Palma de Mallorca, Spain

Received  January 2008 Revised  June 2008 Published  April 2009

Quadratic perturbations of a one-parameter family of quadratic reversible systems with two centers (without other singularities in finite plane) are studied. The exact upper bound of the number of limit cycles, the configurations of limit cycles, and the bifurcation diagrams for different range of the parameter are given.
Keywords: limit cycle., Abelian integral, Quadratic Reversible system.
Mathematics Subject Classification: Primary: 34C07, 34C08; Secondary: 37G1.
Citation: B. Coll, Chengzhi Li, Rafel Prohens. Quadratic perturbations of a class of quadratic reversible systems with two centers. Discrete and Continuous Dynamical Systems, 2009, 24 (3) : 699-729. doi: 10.3934/dcds.2009.24.699
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