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 Integrability and limit cycles of a symmetric 3-dim quadratic system Yongjun Li,Valery G. Romanovski,Dongmei Xiao Keywords:Integrability, limit cycle, bifurcation, polynomial system Abstract: We study periodic solutions and rst integrals in a three-dimensional quadratic system of ODEs. Coecient conditions for existence of centers on center manifolds are obtained. Some bounds of the number of limit cycles bifurcating from the centers under small perturbations are given.