Center Problems and Limit Cycle Bifurcations in a Class of Quasi-Homogeneous Systems
An autonomous system of ordinary differential equations resolved with respect to derivatives is considered. To study its local integrability in a neighborhood of a degenerate stationary point, an approach based on the power geometry method is used. In a previous work, for some two-dimensional system depending on five parameters, a complete set of conditions on these parameters that are necessary conditions of local integrability of the considered system near a strongly degenerate stationary point was found. In this work, it is shown that these conditions are sufficient for global integrability of the system, and the corresponding first integrals of motion are found by using computer algebra tools.