The redemption of singularity confinement
The redemption of singularity confinement
复制标题
奇点禁闭的救赎
DOI：
10.1088/1751-8113/48/11/11ft02
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
間瀬崇史
中科院分区：
文献类型：
--
作者：
K. Shiraga;H. Naito;T. Suzuki;N. Kondo and Y. Ogawa;間瀬崇史
我们提出了一种新的方法来应用奇异禁闭性质作为离散可积性准则。我们将使用我们称之为完全去奇异化的方法，该方法包括将映射中的自由参数作为自变量的函数来处理，应用于补充了原始映射中不存在但不改变奇点结构的项的映射。我们将显示，在主机上的例子，包括著名的映射Hietarinta-Viallet，我们的方法提供了一种方法来计算这些映射的代数熵准确，从而允许一个区分可积和不可积的情况下，即使都有限制奇点。
We present a novel way to apply the singularity confinement property as a discrete integrability criterion. We shall use what we call a full deautonomization approach, which consists in treating the free parameters in the mapping as functions of the independent variable, applied to a mapping complemented with terms that are absent in the original mapping but which do not change the singularity structure. We shall show, on a host of examples including the well-known mapping of Hietarinta–Viallet, that our approach offers a way to compute the algebraic entropy for these mappings exactly, thereby allowing one to distinguish between the integrable and non-integrable cases even when both have confined singularities.