Laurent Polynomials and Superintegrable Maps

Details Laurent Polynomials and Superintegrable Maps Laurent Polynomials and Superintegrable Maps

2007-02-10

arxiv.org/abs/math/0702280v1

SIGMA 3 (2007), 022, 18 pages

Mathematics

Number Theory

This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Sym

Scientific paper

10.3842/SIGMA.2007.022

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.

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