Linearizable mappings

Integrability in discrete-time systems can assume various forms. This work deals with mappings that can be linearized, that is, mappings the solution of which can be obtained from the solution of linear difference equations. We start with the discrete analogue of the Riccati equation and then proceed to examine the discrete forms of second-order linearizable equations. Our investigation is guided by the recently developed “singularity confinement” method that serves as an integrability detector for discrete-time systems.