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

Pages: 699 - 729, Volume 24, Issue 3, July 2009

doi:10.3934/dcds.2009.24.699       Abstract        Full Text (386.9K)

B. Coll - Dept. de Matemàtiques i Informàtica, Universitat de les Illes Balears, Escola Politècnica Superior, 07122-Palma de Mallorca, Spain (email)
Chengzhi Li - School of Mathematical Sciences and LMAM, Peking University, Beijing, 100871, China (email)
Rafel Prohens - Dep. de Matemàtiques i Informàtica. Univ. de Illes Balears, 07122-Palma de Mallorca, Spain (email)

Abstract: 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:  Quadratic Reversible system, Abelian integral, limit cycle.
Mathematics Subject Classification:  Primary: 34C07, 34C08; Secondary: 37G15.

Received: January 2008;      Revised: June 2008;      Published: April 2009.