Periodic solutions for certain systems of planar complex polynomial equations. (Q1812204)

The author deals with the existence of T-periodic solutions to the T-periodic system of complex planar equations \(u'=p_{1}(t,u,v)\), \(v'=p_{2}(t,u,v),\) where \(p_{1}\) and \(p_{2}\) are second-order polynomial whose coefficients are T-periodic continuous functions from \(\mathcal C\). The coefficients of the polynomials have a holomorphic extension to a neighbourhood of the unit disc. An existence theorem for periodic solutions is derived, and this theorem is applied to some generalization of complex periodic Riccati equations.