We present an integrability criterion for rational mappings based on two requirements. First, that a given point should have a unique preimage under the mapping and, second, that the spontaneously appearing singularities be confined to a few iteration steps. We present several examples of known integrable mappings that meet these requirements and, also, use our algorithm in order to derive new examples of integrable mappings.
@article{arxiv.solv-int/9402001,
title = {Non Proliferation of Preimages in Integrable Mappings},
author = {B. Grammaticos and A. Ramani and K. M. Tamizhmani},
journal= {arXiv preprint arXiv:solv-int/9402001},
year = {2009}
}