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Continuous and Discrete Linearizable Systems: The Riccati Saga

  • B. Grammaticos
  • A. Ramani
Part of the CRM Series in Mathematical Physics book series (CRM)

Abstract

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.

Keywords

Riccati Equation Singular Behavior Discrete Linearisable System Matrix Riccati Equation Confinement Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • B. Grammaticos
  • A. Ramani

There are no affiliations available

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