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arxiv: solv-int/9402001 · v1 · submitted 1994-02-10 · solv-int · nlin.SI

Non Proliferation of Preimages in Integrable Mappings

B. Grammaticos (LPN , Universit\'e Paris VII , Tour 24-14 , Paris , France) , A. Ramani (CPT , Ecole polytechnique , CNRS
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UPR 14 91128 Palaiseau K.M. Tamizhmani (Departement of Mathematics Pondicherry University 605014 Pondicherry India)
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classification solv-int nlin.SI
keywords mappingsintegrableexamplesrequirementsalgorithmappearingconfinedcriterion
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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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