关于非交换跳蛙映射
On non-commutative leapfrog map
AI总结：
本文研究非交换跳蛙映射的可积性，通过非交换交比推导显式公式与离散零曲率方程，从非交换洛朗双正交多项式角度分析其连续极限，并借助非交换网络构造泊松结构。
摘要：
本文研究了非交换跳蛙映射的可积性。首先，我们利用非交换交比的概念，推导出非交换跳蛙映射的显式公式及相应的离散零曲率方程。然后，我们从非交换洛朗双正交多项式的角度重新审视了这个离散映射及其连续极限。最后，借助非交换网络，我们构造了该离散非交换映射的泊松结构。通过这些分析与构造，我们旨在加深对非交换跳蛙映射的可积性性质及其相关数学结构的理解。
英文摘要：
We investigate the integrability of the non-commutative leapfrog map in this paper. Firstly, we derive the explicit formula for the non-commutative leapfrog map and corresponding discrete zero-curvature equation by employing the concept of non-commutative cross-ratio. Then we revisit this discrete map, as well as its continuous limit, from the perspective of non-commutative Laurent bi-orthogonal polynomials. Finally, the Poisson structure for this discrete non-commutative map is formulated with the help of a non-commutative network. We aim to enhance our understanding of the integrability properties of the non-commutative leapfrog map and its related mathematical structures through these analysis and constructions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
