A Study of the Continuous and Discrete Gambier Systems

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dc.creatorRamani, A.
dc.creatorGrammaticos, B.
dc.creatorLafortune, S.
dc.date2001-04-06
dc.date.accessioned2026-07-07T05:33:24Z
dc.date.available2026-07-07T05:33:24Z
dc.descriptionWe present a systematic study of the Gambier system, which in the continuous case is given by two Riccati equations in cascade. We derive the condition for its integrability and show that the generic Gambier system contains one free function. We also derive the Schlesinger transformations for this system which allows in principle the systematic construction of the integrable cases. The above procedure is carried over to a discrete setting. We show thus how the discrete Gambier system can be expressed as a system of two homographic mappings in cascade. The integrable cases are obtained through the singularity confinement discrete integrability criterion. Finally the discrete Schlesinger transformations are also derived giving a handle to the construction of the integrable Gambier mapping.
dc.description15 pages, no figure
dc.identifierhttps://arxiv.org/abs/nlin/0104017
dc.identifierhttp://arxiv.org/abs/nlin/0104017
dc.identifierSIDE III - Symmetry and Integrability of Difference Equations (Decio Levi and Orlando Ragnisco, eds.) (Conference held in Italy, 1998), CRM Proc. Lectures Notes, vol.25, Amer. Math. Soc., Providence, RI (2000), 367-379
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79984
dc.subjectExactly Solvable and Integrable Systems
dc.titleA Study of the Continuous and Discrete Gambier Systems
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