论文标题
Wynn复发的整合性和几何形状
Integrability and geometry of the Wynn recurrence
论文作者
论文摘要
我们表明，可以将Wynn复发（Padé近似理论的Frobenius的缺失身份）纳入可集成系统的理论中，以减少离散的Schwarzian Kadomtsev-Petviashvili方程。这尤其允许将复发的几何含义作为适当约束的四角集点组的结构。该解释对于在任意偏斜场上的投影线是有效的，它激发了考虑非交流性帕德理论的动机。我们使用准固定剂将相应的元素（包括Frobenius身份）转移到非交通级别。使用斐波那契语言的特征系列的示例，我们介绍了该理论对普通语言的应用。我们介绍了离散时间TODA晶格方程的非交通性版本及其集成性结构。最后，我们讨论了永利复发在离散分析函数几何理论的不同背景下的应用。
We show that the Wynn recurrence (the missing identity of Frobenius of the Padé approximation theory) can be incorporated into the theory of integrable systems as a reduction of the discrete Schwarzian Kadomtsev-Petviashvili equation. This allows, in particular, to present the geometric meaning of the recurrence as a construction of the appropriately constrained quadrangular set of points. The interpretation is valid for a projective line over arbitrary skew field what motivates to consider non-commutative Padé theory. We transfer the corresponding elements, including the Frobenius identities, to the non-commutative level using the quasideterminants. Using an example of the characteristic series of the Fibonacci language we present an application of the theory to the regular languages. We introduce the non-commutative version of the discrete-time Toda lattice equations together with their integrability structure. Finally, we discuss application of the Wynn recurrence in a different context of the geometric theory of discrete analytic functions.
