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- W97878893 abstract "We present a review of what is current knowledge about discrete Painlevé equations. We start with a historical introduction which explains how the discrete Painlevé equations made their appearance. Since the most widely used derivation method was the one based on integrability detectors, we start by presenting a brief review of the existing discrete integrability detectors, and proceed to show how they were indeed used in deriving the discrete Painlevé equations. Given the profusion of different forms of these mappings, we examine the various approaches to their classification, from the first, crude ones, to the complete classification based on affine Weyl groups. The properties of the discrete Painlevé equations, which make them so special, are also reviewed with ample details. Finally, we present a series of results which are peripherally related to the discrete Painlevé equations but help cast more light on these (very) special systems." @default.
- W97878893 created "2016-06-24" @default.
- W97878893 creator A5025004511 @default.
- W97878893 creator A5062941446 @default.
- W97878893 date "2004-06-09" @default.
- W97878893 modified "2023-10-05" @default.
- W97878893 title "Discrete Painlevé Equations: A Review" @default.
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- W97878893 doi "https://doi.org/10.1007/978-3-540-40357-9_7" @default.
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