# Georgios Papamikos: Yang-Baxter maps, integrable maps and generalisations

We present some solutions of the set-theoretic parametric Yang-Baxter equation. These solutions are birational maps with several invariants and a Lax representation[4]. We show that we can use these maps as building blocks in order to construct higher dimensional birational maps which have nice properties and we prove their integrability in the Liouville sense. These maps can be seen as higher dimensional generalisations of the famous integrable QRT maps [3], known as Adler’s Triad maps[1]. Finally, we discuss some new generalisations [2].

- Georgios Papamikos:
*University of Essex*

References [1] V. E. Adler, On a class of third order mappings with two rational invariants, preprint, arXiv:nlin/0606056v1 [2] S. Konstantinou-Rizos, G.Papamikos, Entwining Yang-Baxter maps related to NLS type equations, Journal of Physics A: Mathematical and Theoretical, 52, 2019 [3] G. R. W. Quispel, J. A. G. Roberts, C. J. Thompson, Integrable mappings and soliton equations II, Physica D: Nonlinear Phenomena34(1989), 183-192. [4] A. P. Veselov, Yang-Baxter maps and integrable dynamics, Physics Letters A314 (2003), 214 - 221.