A survey of nonsymmetric Riccati equations

We prove a fundamental representation formula for all solutions of the matrix Riccati differential equation (RDE) and of the corresponding algebraic Riccati equation (ARE). This formula contains the complete information on the phase portrait of (RDE) and on the structure of the set Γ of all solutions of (ARE). In particular we describe all con-stant, periodic and almost periodic solutions of (RDE). Further we give an application of the fundamental representation formula to the investigation of nonautonomous Riccati equations