Non Proliferation of Preimages in Integrable Mappings
  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. 
B. Grammaticos (LPN, Universit\'e Paris VII, Tour 24-14, Paris,   France), A. Ramani (CPT, Ecole Polytechnique, CNRS, UPR 14...