On the explicit integration of a class of linearizable mappings
On the explicit integration of a class of linearizable mappings
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关于一类可线性化映射的显式积分
DOI：
10.1088/1751-8113/45/36/365202
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
A.Ramani
中科院分区：
文献类型：
--
作者：
K. Yamaguchi;M. Kawakita;N. Takahashi and J. Takeuchi;Toshio Nagashima;A.Ramani
本文研究了一类二阶映射，它可以通过化为线性方程来积分。这些映射已经确定在我们以前的工作中，我们已经精确地显示了如何获得其线性化。属于这类的映射称为“第三类可线性化映射”。我们构造了它们的显式解，并得到了它们的一个非自治的QRT不变量。我们发现，这些“第三类”映射是有关的另一类线性映射，称为映射的Gambier型，从他们获得通过（离散）衍生物相对于一个参数。
We examine a class of second-order mappings which can be integrated by reduction to a linear equation. These mappings have been identified in our previous works where we have precisely shown how to obtain their linearization. The mappings belonging to this class are referred to as' linearizable mappings of the third kind'. We construct their explicit solution and obtain, for all of them, an invariant of QRT aspect but which is non-autonomous. We show that some of these'third-kind'mappings are related to another class of linearizable mappings, known as mappings of Gambier type, from which they are obtained through a (discrete) derivative with respect to a parameter.