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 Volume 1, Number 1, 2011, Pages 9-20                                                                DOI：10.11948/2011002 Integrability conditions for complex systems with homogeneous Brigita Ferčec,Xingwu Chen,Valery G. Romanovski Keywords:Integrability, center problem, time-reversibility, polynomial vector field , Darbouxintegral. Abstract: In this paper we obtain conditions for the existence  of a local analytic first integral for four eight-parameter families of quintic complex system. We also discuss computational difficulties arising in the study of the problem of integrability for these systems. PDF      Download reader