Non Proliferation of Preimages in Integrable Mappings
arXiv:solv-int/9402001 · doi:10.1088/0305-4470/27/2/037
Abstract
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.
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