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QRT maps and related Laurent systems

Hamad, K., Hone, Andrew N.W., van der Kamp, Peter H., Quispel, G.R.W. (2018) QRT maps and related Laurent systems. Advances in Applied Mathematics, 96 . pp. 216-248. ISSN 0196-8858. (doi:10.1016/j.aam.2017.12.006) (KAR id:66438)

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In recent work it was shown how recursive factorisation of certain QRT maps leads to Somos-4 and Somos-5 recurrences with periodic coefficients, and to a fifth-order recurrence with the Laurent property. Here we recursively factorise the 12-parameter symmetric QRT map, given by a second-order recurrence, to obtain a system of three coupled recurrences which possesses the Laurent property. As degenerate special cases, we first derive systems of two coupled recurrences corresponding to the 5-parameter multiplicative and additive symmetric QRT maps. In all cases, the Laurent property is established using a generalisation of a result due to Hickerson, and exact formulae for degree growth are found from ultradiscrete (tropical) analogues of the recurrences. For the general 18-parameter QRT map it is shown that the components of the iterates can be written as a ratio of quantities that satisfy the same Somos-7 recurrence.

Item Type: Article
DOI/Identification number: 10.1016/j.aam.2017.12.006
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Funders: Engineering and Physical Sciences Research Council (
Depositing User: Andrew Hone
Date Deposited: 16 Mar 2018 18:49 UTC
Last Modified: 09 Jan 2024 16:57 UTC
Resource URI: (The current URI for this page, for reference purposes)

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