Symplectic Maps from Cluster Algebras
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Symplectic Maps from Cluster Algebras
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| Creator |
Fordy, A.P.
Hone, A. |
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| Description |
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.
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| Date |
2019-02-14T17:28:43Z
2019-02-14T17:28:43Z 2011 |
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| Type |
Article
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| Identifier |
Symplectic Maps from Cluster Algebras / A.P. Fordy, A. Hone // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 17 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 37K10; 17B63; 53D17; 14T05 http://dx.doi.org/10.3842/SIGMA.2011.091 http://dspace.nbuv.gov.ua/handle/123456789/147396 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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