Continuous and Discrete Linearizable Systems: The Riccati Saga
We investigate the extensions of the discrete Riccati equation, as a linearizable system, to higher dimensions. We first study the continuous and discrete (second-order) Gambier equation, which is a coupling of two Riccati equations in cascade. In the N-dimensional case, three new integrable mappings are obtained: they are the linearizable discretizations of the well-known projective, matrix, and conformai Riccati systems.
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