Discrete matrix Riccati equations with superposition formulas

Abstract:
An ordinary differential equation is said to have a superposition formula if its general solution can be expressed as a function of a finite number of particular solution. Nonlinear ODE's with superposition formulas include matrix Riccati equations. Here will shall describe discretizations of Riccati equations that preserve the superposition formulas. The approach is general enough to include q-derivatives and standard discrete derivatives. The work was done jointly with Pavel Winternitz.