Generalised QRT mappings with periodic coefficients
Generalised QRT mappings with periodic coefficients
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具有周期系数的广义 QRT 映射
DOI：
10.1088/0951-7715/24/1/006
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发表时间：
2011
期刊：
影响因子：
1.7
通讯作者：
B. Grammaticos and R. Willox
中科院分区：
文献类型：
--
作者：
A. Ramani;B. Grammaticos and R. Willox
我们提出了一个扩展的QRT映射超出熟悉的对称和不对称品种。从离散Painlevé方程的结果出发，证明了存在系数为周期函数的可积类QRT映射.本文给出了几个具有不同周期系数的映射的例子，并证明了存在周期为任意长的情形。我们证明了所有的例子，通过构建相应的守恒量的可积性，我们展示了如何这些系统，就像他们的QRT兄弟姐妹，可以明确集成的椭圆函数。
We present an extension of the QRT mapping beyond the familiar symmetric and asymmetric varieties. Starting from our results on discrete Painlevé equations, we show that there exist integrable QRT-like mappings, the coefficients of which are periodic functions. We present several examples of mappings with periodic coefficients of various periods and show that there exist cases where the periods are arbitrarily long. We prove the integrability of all the examples by constructing the corresponding conserved quantities and we show how these systems, just as their QRT siblings, can be explicitly integrated in terms of elliptic functions.