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arXiv · 2310.01993

On non-commutative leapfrog map

Bao Wang·Shi-Hao Li
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Abstract

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.

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Bao Wang, Shi-Hao Li. 2023-10-03. On non-commutative leapfrog map. https://arxiv.org/abs/2310.01993

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