Non-integrability by discrete quadratures

被引：2

作者：

Casale, Guy ^{[1
]}

Roques, Julien ^{[2
]}

机构：

[1] Univ Rennes 1, UMR 6625, IRMAR, F-35042 Rennes, France

[2] Univ Grenoble 1, CNRS, UMR 5582, Inst Fourier, F-38402 St Martin Dheres, France

来源：

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2014年 / 687卷

关键词：

DIFFERENTIAL GALOIS THEORY; PAINLEVE-III EQUATION; INTEGRABILITY; SYSTEMS;

D O I：

10.1515/crelle-2012-0054

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：87 / 112

页数：26

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