Branquinho, A.Rebocho, M. N.2020-02-062020-02-062010A. Branquinho and M.N. Rebocho, Matrix Sylvester equations in the theory of orthogonal polynomials on the unit circle, Bulletin of the Belgian Mathematical Society - Simon Stevin 17 (2010), 355-376.http://hdl.handle.net/10400.6/9055In this paperwe characterize sequences of orthogonal polynomials on the unit circle whose Carathéodory function satisfies a Riccati differential equation with polynomial coefficients, in terms of matrix Sylvester differential equations. For the particular case of semi-classical orthogonal polynomials on the unit circle, it is derived a characterization in terms of first order linear differential systems.engOrthogonal polynomials on the unit circleMatrix Sylvester differential equationsMatrix Riccati differential equationsMeasures on the unit circleSemi-classical classjournal article