Resumen de Bifurcation of Limit Cycles and Pseudo-Isochronicity at Infinity in a Septic Polynomial Vector Field

Yusen Wu, Luju Liu

• In this paper, we study the appearance of limit cycles from the equator and pseudo-isochronicity at infinity in a class of septic polynomial vector field with no singular point at infinity. We solve the problems by an indirect method, i.e., we transform infinity into the origin so that we can investigate the properties of infinity with the methods developed for finite critical point. Further, we construct a septic system which has six limit cycles in the neighborhood of infinity. Finally, we investigate the pseudo-isochronous center conditions at infinity for the system. As far as we know, this is the first time that the bifurcation of limit cycles and pseudo-isochronous center conditions at infinity in a septic system are simultaneously discussed.