Resumen de Analytically Integrable Centers of Perturbations of Cubic Homogeneous Systems

Antonio Algaba Durán, Cristóbal García García, Manuel Reyes Columé

• We consider the analytically integrable perturbations of cubic homogeneous differential systems whose origin is an isolated singularity. We prove that are orbitally equivalent to the cubic vector field associated. We also characterize the analytically integrable centers. We apply the results to two families of degenerate vector fields.