Fiber-dependent deautonomization of integrable 2D mappings and discrete Painleve equations
Fiber-dependent deautonomization of integrable 2D mappings and discrete Painleve equations
复制标题
可积二维映射和离散 Painleve 方程的光纤相关去自治化
DOI：
10.1088/1751-8121/aa86c3
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Tomoyuki Takenawa
中科院分区：
文献类型：
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作者：
Adrian Stefan Carstea;Anton Dzhamay;Tomoyuki Takenawa
众所周知，二维映射保持有理椭圆纤维化，如Quispel-Roberts-Thompson映射，可以离散Painlevé方程。然而，这一过程对特定椭圆光纤的选择的依赖性还没有得到充分的研究。本文建立了一种对一个自治映射和一个纤维进行去重化的方法。从一个单一的自治映射，但不同类型的所选纤维，我们得到不同类型的离散Painlevé方程使用此去卷积过程。我们还介绍了一种技术，用于重建映射的知识，其诱导行动的皮卡德组和一些额外的几何数据。这种技术使我们能够获得离散Painlevé方程的因式分解表达式，包括椭圆情况。此外，通过对这种非自治映射施加一定的限制，我们得到新的和简单的椭圆差分Painlevé方程，包括对称群没有明确出现在Sakai的分类的例子。
It is well known that two-dimensional mappings preserving a rational elliptic fibration, like the Quispel–Roberts–Thompson mappings, can be deautonomized to discrete Painlevé equations. However, the dependence of this procedure on the choice of a particular elliptic fiber has not been sufficiently investigated. In this paper we establish a way of performing the deautonomization for a pair of an autonomous mapping and a fiber. Starting from a single autonomous mapping but varying the type of a chosen fiber, we obtain different types of discrete Painlevé equations using this deautonomization procedure. We also introduce a technique for reconstructing a mapping from the knowledge of its induced action on the Picard group and some additional geometric data. This technique allows us to obtain factorized expressions of discrete Painlevé equations, including the elliptic case. Further, by imposing certain restrictions on such non-autonomous mappings we obtain new and simple elliptic difference Painlevé equations, including examples whose symmetry groups do not appear explicitly in Sakai's classification.