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dc.contributor.author Fordy, A.P.
dc.contributor.author Hone, A.
dc.date.accessioned 2019-02-14T17:28:43Z
dc.date.available 2019-02-14T17:28:43Z
dc.date.issued 2011
dc.identifier.citation Symplectic Maps from Cluster Algebras / A.P. Fordy, A. Hone // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 17 назв. — англ. uk_UA
dc.identifier.issn 1815-0659
dc.identifier.other 2010 Mathematics Subject Classification: 37K10; 17B63; 53D17; 14T05
dc.identifier.other http://dx.doi.org/10.3842/SIGMA.2011.091
dc.identifier.uri http://dspace.nbuv.gov.ua/handle/123456789/147396
dc.description.abstract We consider nonlinear recurrences generated from the iteration of maps that arise from cluster algebras. More precisely, starting from a skew-symmetric integer matrix, or its corresponding quiver, one can define a set of mutation operations, as well as a set of associated cluster mutations that are applied to a set of affine coordinates (the cluster variables). Fordy and Marsh recently provided a complete classification of all such quivers that have a certain periodicity property under sequences of mutations. This periodicity implies that a suitable sequence of cluster mutations is precisely equivalent to iteration of a nonlinear recurrence relation. Here we explain briefly how to introduce a symplectic structure in this setting, which is preserved by a corresponding birational map (possibly on a space of lower dimension). We give examples of both integrable and non-integrable maps that arise from this construction. We use algebraic entropy as an approach to classifying integrable cases. The degrees of the iterates satisfy a tropical version of the map. uk_UA
dc.description.sponsorship This paper is a contribution to the Proceedings of the Conference “Symmetries and Integrability of Difference Equations (SIDE-9)” (June 14–18, 2010, Varna, Bulgaria). The full collection is available at http://www.emis.de/journals/SIGMA/SIDE-9.html. The authors would like to thank the Isaac Newton Institute, Cambridge for hospitality during the Programme on Discrete Integrable Systems, where this collaboration began. They are also grateful to the organisers of SIDE 9 in Varna for inviting us both to speak there. uk_UA
dc.language.iso en uk_UA
dc.publisher Інститут математики НАН України uk_UA
dc.relation.ispartof Symmetry, Integrability and Geometry: Methods and Applications
dc.title Symplectic Maps from Cluster Algebras uk_UA
dc.type Article uk_UA
dc.status published earlier uk_UA

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