This article is cited in 8 papers

Integrable extensions of the Adler map via Grassmann algebras

P. Adamopoulou^a, S. Konstantinou-Rizos^b, G. Papamikos<sup>c

a</sup> School of Mathematical and Computer Sciences, Heriot–Watt University, UK
^b Centre of integrable systems, Demidov Yaroslavl State University, Russia
^c Department of Mathematical Sciences, University of Essex, UK

Abstract: We study certain extensions of the Adler map on Grassmann algebras $\Gamma(n)$ of order $n$. We consider a known Grassmann-extended Adler map and under the assumption that $n=1$, obtain a commutative extension of the Adler map in six dimensions. We show that the map satisfies the Yang–Baxter equation, admits three invariants, and is Liouville integrable. We solve the map explicitly by regarding it as a discrete dynamical system.

Keywords: Yang–Baxter map, Grassmann algebra, Liouville integrability, solution of discrete dynamical system, symplectic structure.

PACS: 02.30.Ik

MSC: 15A75, 35Q53, 16T25, 17B80, 37J70

Received: 25.12.2020
Revised: 25.12.2020

DOI: 10.4213/tmf10045

 English version: Theoretical and Mathematical Physics, 2021, 207:2, 553–559

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