Fordy, AP orcid.org/0000-0002-2523-0262 (2011) Mutation-periodic quivers, integrable maps and associated Poisson algebras. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 369 (1939). pp. 1264-1279. ISSN 1364-503X
Abstract
We consider a class of map, recently derived in the context of cluster mutation. In this paper, we start with a brief review of the quiver context, but then move onto a discussion of a related Poisson bracket, along with the Poisson algebra of a special family of functions associated with these maps. A bi-Hamiltonian structure is derived and used to construct a sequence of Poisson-commuting functions and hence show complete integrability. Canonical coordinates are derived, with the map now being a canonical transformation with a sequence of commuting invariant functions. Compatibility of a pair of these functions gives rise to Liouville’s equation and the map plays the role of a Bäcklund transformation.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2011, The Royal Society. This is an author produced version of a article published in Philosophical Transactions A: Mathematical, Physical and Engineering Sciences. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Poisson algebra; bi-Hamiltonian; integrable map; Bäcklund transformation; Laurent property; cluster algebra |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 22 May 2019 10:10 |
Last Modified: | 24 May 2019 17:11 |
Status: | Published |
Publisher: | The Royal Society |
Identification Number: | 10.1098/rsta.2010.0318 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:119303 |