The center conditions and bifurcation of limit cycles at the infinity for a cubic polynomial system (Q648330)

The paper deals with the problem of center conditions and bifurcation of limit cycles at the infinity for a class of cubic systems. By using a homeomorphic transformation of the infinity into the origin and applying the computer algebra system \texttt{Mathematica}, conditions for the origin to be a center are derived and the \(21\)-st fine focus conditions are computed. The authors construct a cubic system where seven limit cycles can bifurcate from the infinity by a small perturbation of parameters. The isochronous center conditions at the infinity for the cubic system are investigated, too.