Linearizable mappings and the low-growth criterion

We examine a family of discrete second-order systems which are integrable t hrough reduction to a linear system. These systems were previously identifi ed using the singularity confinement criterion. Here we analyse them using the more stringent criterion of nonexponential growth of the degrees of the iterates. We show that the linearizable mappings are characterized by a ve ry special degree growth. The ones linearizable by reduction to projective systems exhibit zero growth, i.e. they behave like linear systems, while th e remaining ones (derivatives of Riccati and Gambler mapping) lead to linea r growth. This feature may well serve as a detector of integrability throug h linearization.