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Elliptic discrete Painlevé equations. (English) Zbl 1056.39027
The geometrical description of discrete Painlevé equations in terms of affine Weyl groups reveals, in the case of those described by \(E_{8}^{(1)}\), along with difference equations and \(q\)-difference equations, the existence of so-called “elliptic” discrete Painlevé equations. The paper under review presents explicit forms of such objects with eight degrees of freedom. It also suggests the probale existence of more than those found here.

MSC:
39A13 Difference equations, scaling (\(q\)-differences)
39A12 Discrete version of topics in analysis
39A70 Difference operators
34M55 Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies
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