Geodesic
Integrable extensions of the~Adler map via Grassmann algebras
Teoretičeskaâ i matematičeskaâ fizika, Tome 207 (2021) no. 2, pp. 179-187

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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. 
@article{TMF_2021_207_2_a0,
     author = {P. Adamopoulou and S. Konstantinou-Rizos and G. Papamikos},
     title = {Integrable extensions of {the~Adler} map via {Grassmann} algebras},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {179--187},
     publisher = {mathdoc},
     volume = {207},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2021_207_2_a0/}
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P. Adamopoulou; S. Konstantinou-Rizos; G. Papamikos. Integrable extensions of the~Adler map via Grassmann algebras. Teoretičeskaâ i matematičeskaâ fizika, Tome 207 (2021) no. 2, pp. 179-187. http://geodesic.mathdoc.fr/item/TMF_2021_207_2_a0/