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Article Dans Une Revue Journal für die reine und angewandte Mathematik Année : 2014

Non-integrability by discrete quadratures

Julien Roques

Résumé

We give a necessary condition for integrability by discrete quadratures of systems of difference equations: the discrete variational equations along algebraic solutions must have virtually solvable Galois groups. This necessary condition a la Morales and Ramis is used in order to prove that q-analogues of Painleve I and Painleve III equations are not integrable by discrete quadratures.
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Dates et versions

hal-00956242 , version 1 (06-03-2014)

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Guy Casale, Julien Roques. Non-integrability by discrete quadratures. Journal für die reine und angewandte Mathematik, 2014, 687, pp.87-112. ⟨10.1515/crelle-2012-0054⟩. ⟨hal-00956242⟩
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