Non Proliferation of Preimages in Integrable Mappings

Nonlinear Sciences – Exactly Solvable and Integrable Systems

Scientific paper

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Scientific paper

10.1088/0305-4470/27/2/037

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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