Polynomial vector fields on algebraic surfaces of revolution (Q2660579)

The authors study polynomial vector fields of arbitrary degree in \(\mathbb{R}^3\) having an algebraic surface of revolution invariant by their flows. Subsequently, they restrict their attention to an important case where the algebraic surface of revolution is a cubic surface and characterize all the possible configurations of invariant meridians and parallels that the vector fields can exhibit. Lastly, they consider when the invariant parallels can be limit cycles.