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The first part of the present paper is devoted to a systematic constructionof continuous-time finite-dimensional integrable systems arising from therational su(2) Gaudin model through certain contraction procedures. In thesecond part, we derive an explicit integrable Poisson map discretizing aparticular Hamiltonian flow of the rational su(2) Gaudin model. Then, thecontraction procedures enable us to construct explicit integrablediscretizations of the continuous systems derived in the first part of thepaper.

An integrable discretization of the rational su(2) Gaudin model and related systems