标题： 格方程的完全非自治化 显示英文标题

标题： Full-deautonomisation of a lattice equation

摘要： 在本通信中，我们报道了一种意外的可能性，即应用我们最近提出的全非自治化方法来预测二阶双有理映射的代数熵，这种方法也可以应用于离散格方程。 此外，我们通过两个例子表明，全非自治化技术实际上也可以成功地应用于这些格方程的约化形式，即阶数高于二的映射。 特别是，我们将此技术应用于最近发现的一个具有限制性奇点但又非可积的格方程，并证明我们的方法能够准确预测其非可积特性。 最后，我们展示了如何利用我们的方法甚至可以预测某些非限制性高阶映射的代数熵。 显示英文摘要

摘要： In this letter we report on the unexpected possibility of applying the full-deautonomisation approach we recently proposed for predicting the algebraic entropy of second-order birational mappings, to discrete lattice equations. Moreover, we show, on two examples, that the full-deautonomisation technique can in fact also be successfully applied to reductions of these lattice equations to mappings with orders higher than 2. In particular, we apply this technique to a recently discovered lattice equation that has confined singularities while being nonintegrable, and we show that our approach accurately predicts this nonintegrable character. Finally, we demonstrate how our method can even be used to predict the algebraic entropy for some nonconfining higher order mappings.