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Teoreticheskaya i Matematicheskaya Fizika, 2021, Volume 207, Number 2, Pages 179–187
DOI: https://doi.org/10.4213/tmf10045 (Mi tmf10045) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Integrable extensions of the Adler map via Grassmann algebras

P. Adamopouloua, S. Konstantinou-Rizosb, G. Papamikosc

a 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
Full-text PDF (447 kB) Citations (6)
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DOI: https://doi.org/10.4213/tmf10045
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.
Funding agency Grant number
Russian Science Foundation 20-71-10110
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).
Received: 25.12.2020
Revised: 25.12.2020
English version:
Theoretical and Mathematical Physics, 2021, Volume 207, Issue 2, Pages 553–559
DOI: https://doi.org/10.1134/S0040577921050019
Bibliographic databases:
Document Type: Article
PACS: 02.30.Ik
MSC: 15A75, 35Q53, 16T25, 17B80, 37J70
Language: Russian
Citation: P. Adamopoulou, S. Konstantinou-Rizos, G. Papamikos, “Integrable extensions of the Adler map via Grassmann algebras”, TMF, 207:2 (2021), 179–187; Theoret. and Math. Phys., 207:2 (2021), 553–559
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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