English

Quadrirational Yang-Baxter maps and the elliptic Cremona system

Exactly Solvable and Integrable Systems 2018-04-06 v1

Abstract

This paper connects the quadrirational Yang-Baxter maps, which are two-dimensional integrable discrete systems of KdV type, and the elliptic Cremona system, which is a higher analogue of discrete Painlev\'e equations associated with E~8\tilde{E}_8 symmetry. This is a natural connection between integrable systems in different dimensions that is outside of the usual paradigm of reductions. Our approach is based on formulation of both systems in terms of birational Coxeter groups.

Keywords

Cite

@article{arxiv.1804.01794,
  title  = {Quadrirational Yang-Baxter maps and the elliptic Cremona system},
  author = {James Atkinson and Yasuhiko Yamada},
  journal= {arXiv preprint arXiv:1804.01794},
  year   = {2018}
}

Comments

11 pages, 2 figures. This is a comprehensive revision of the previous (unpublished) work arXiv:1405.2745

R2 v1 2026-06-23T01:14:48.463Z