TY - JOUR
T1 - Integrable extensions of the Adler map via Grassmann algebras
AU - Adamopoulou, Panagiota-Maria
AU - Konstantinou-Rizos, Sotiris
AU - Papamikos, Georgios
N1 - Funding Information:
∗School of Mathematical and Computer Sciences, Heriot–Watt University, UK, e-mail: [email protected]. †Centre of Integrable Systems, Demidov Yaroslavl State University, Russia, e-mail: [email protected] (corresponding author). ‡Department of Mathematical Sciences,University of Essex, UK, e-mail: [email protected]. This research started while S. Konstantinou-Rizos visited Heriot-Watt University in January 2019 and the University of Essex on an International Visiting Fellowship in November 2019. The research of S. Konstantinou-Rizos was supported by a grant from the Russian Science Foundation (Project No. 20-71-10110).
Publisher Copyright:
© 2021 Pleiades Publishing, Ltd.
PY - 2021/6/21
Y1 - 2021/6/21
N2 - We study certain extensions of the Adler map on Grassmann algebras Γ(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.
AB - We study certain extensions of the Adler map on Grassmann algebras Γ(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.
KW - Grassmann algebra
KW - Liouville integrability
KW - Solution of discrete dynamical system
KW - Symplectic structure
KW - Yang–Baxter map
UR - http://www.scopus.com/inward/record.url?scp=85111444649&partnerID=8YFLogxK
U2 - 10.1134/S0040577921050019
DO - 10.1134/S0040577921050019
M3 - Article
SN - 0040-5779
VL - 207
SP - 553
EP - 559
JO - Theoretical and Mathematical Physics
JF - Theoretical and Mathematical Physics
IS - 2
ER -