ИСТИНА

We consider an autonomous system of ordinary differential equations, which is resolved with respect to derivatives. To study local integrability of the system near a degenerate stationary point, we use an approach based on the power geometry [Bruno:1998] and the computation of the resonant normal form [Bruno:1979,Edneral:2007]. For the partial non Hamilton 5-parameter case of the Algaba system [Algaba:2009] planar system, we have found the complete set of necessary conditions on parameters of the system for which the system is locally integrable near a degenerate stationary point. These sets of parameters, satisfying the conditions, consist of 4 two-parameter subsets in this 5-parameter space. For these subsets, we found analytic global first integrals of the system [BrunoEdneral:2013]. In this report we describe the possible way for investigation of others non Hamilton 5-parameter cases of the Algaba system.