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Laurent Polynomials and Superintegrable Maps

Hone, Andrew N.W. (2007) Laurent Polynomials and Superintegrable Maps. Symmetry, Integrability and Geometry: Methods and Applications, 3 (022). pp. 1-18. ISSN 1815-0659. (KAR id:41491)

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Abstract

This article is dedicated to the memory of Vadim Kuznetsov, and begins with some of the author's recollections of him. Thereafter, a brief review of Somos sequences is provided, with particular focus being made on the integrable structure of Somos-4 recurrences, and on the Laurent property. Subsequently a family of fourth-order recurrences that share the Laurent property are considered, which are equivalent to Poisson maps in four dimensions. Two of these maps turn out to be superintegrable, and their iteration furnishes infinitely many solutions of some associated quartic Diophantine equations.

Item Type: Article
Subjects: Q Science > QA Mathematics (inc Computing science) > QA150 Algebra
Q Science > QA Mathematics (inc Computing science) > QA150 Algebra > QA241 Number theory
Q Science > QC Physics > QC20 Mathematical Physics
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Andrew Hone
Date Deposited: 21 Jun 2014 01:04 UTC
Last Modified: 06 Feb 2020 04:09 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/41491 (The current URI for this page, for reference purposes)
Hone, Andrew N.W.: https://orcid.org/0000-0001-9780-7369
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