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March  2006, 16(1): 157-177. doi: 10.3934/dcds.2006.16.157

The cyclicity of period annuli of some classes of reversible quadratic systems

G. Chen 1, , C. Li 2, , C. Liu 1, and  Jaume Llibre 3,

1. 

UFR de Mathématiques, Laboratoire P. Painlevé, UMR 8524, Université de Lille 1, 59655 Villeneuve d’Ascq, France, France
2. 

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

Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, 08193 Barcelona

Received  January 2005 Revised  March 2006 Published  June 2006

The cyclicity of period annuli of some classes of reversible and non-Hamiltonian quadratic systems under quadratic perturbations are studied. The argument principle method and the centroid curve method are combined to prove that the related Abelian integral has at most two zeros.
Keywords: reversible systems, Limit cycle, Abelian integral..
Mathematics Subject Classification: Primary: 34C07, 34C08; Secondary: 37G1.
Citation: G. Chen, C. Li, C. Liu, Jaume Llibre. The cyclicity of period annuli of some classes of reversible quadratic systems. Discrete & Continuous Dynamical Systems, 2006, 16 (1) : 157-177. doi: 10.3934/dcds.2006.16.157
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