The last remake of the Gambier mapping

S. Lafortune, A. Ramani and B. Grammaticos

Physica A: Statistical Mechanics and its Applications, 2003, vol. 317, issue 3, 383-390

Abstract: We present a special discrete analogue of the Gambier coupled-Riccati system where the coupling is introduced in an additive way. We show that there exist choices of the parameters for which the singularities of the mapping are confined. Computing the continuous limit of the mapping we show that the resulting differential equation never possesses the Painlevé property. We present an explanation of this apparent paradox.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:317:y:2003:i:3:p:383-390

DOI: 10.1016/S0378-4371(02)01355-9

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