Abstract
We investigate generalizations of the discrete Riccati equation as a linearizable system, to multicomponent linearizable systems. These are discretizations of nonlinear ordinary differential equations with superposition formulas. We present discrete matrix Riccati equations, projective, conformal, orthogonal and symplectic Riccati equations. Also obtained are discrete equations, based on complex orthogonal and symplectic groups, that in the continuous limit involve fourth order polynomial nonlinearities. All these equations satisfy the criterion of singularity confinement.
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