Integrable extensions of the Adler map via Grassmann algebras

Panagiota-Maria Adamopoulou, Sotiris Konstantinou-Rizos, Georgios Papamikos

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)553–559
Number of pages7
JournalTheoretical and Mathematical Physics
Volume207
Issue number2
DOIs
Publication statusPublished - 21 Jun 2021

Keywords

  • Grassmann algebra
  • Liouville integrability
  • Solution of discrete dynamical system
  • Symplectic structure
  • Yang–Baxter map

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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