Laurent Polynomials and Superintegrable Maps

Laurent Polynomials and Superintegrable Maps

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. Sub...

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Bibliographic Details
Main Author: Andrew N.W. Hone
Format: Article
Language:English
Published: National Academy of Science of Ukraine 2007-02-01
Series:Symmetry, Integrability and Geometry: Methods and Applications
Subjects:
Laurent property
integrable maps
Somos sequences
Online Access:http://www.emis.de/journals/SIGMA/2007/022/
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spelling doaj-f54a02f56be742678303b194266362142020-11-25T00:39:36ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592007-02-013022Laurent Polynomials and Superintegrable MapsAndrew N.W. HoneThis 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.http://www.emis.de/journals/SIGMA/2007/022/Laurent propertyintegrable mapsSomos sequences
collection DOAJ
language English
format Article
sources DOAJ
author Andrew N.W. Hone
spellingShingle Andrew N.W. Hone
Laurent Polynomials and Superintegrable Maps
Symmetry, Integrability and Geometry: Methods and Applications
Laurent property
integrable maps
Somos sequences
author_facet Andrew N.W. Hone
author_sort Andrew N.W. Hone
title Laurent Polynomials and Superintegrable Maps
title_short Laurent Polynomials and Superintegrable Maps
title_full Laurent Polynomials and Superintegrable Maps
title_fullStr Laurent Polynomials and Superintegrable Maps
title_full_unstemmed Laurent Polynomials and Superintegrable Maps
title_sort laurent polynomials and superintegrable maps
publisher National Academy of Science of Ukraine
series Symmetry, Integrability and Geometry: Methods and Applications
issn 1815-0659
publishDate 2007-02-01
description 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.
topic Laurent property
integrable maps
Somos sequences
url http://www.emis.de/journals/SIGMA/2007/022/
work_keys_str_mv AT andrewnwhone laurentpolynomialsandsuperintegrablemaps
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