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On the Hamiltonian structure of Hirota-Kimura discretization of the Euler top

✍ Scribed by Matteo Petrera; Yuri B. Suris

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
93 KB
Volume
283
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

This paper deals with a remarkable integrable discretization of the so (3) Euler top introduced by Hirota and Kimura. Such a discretization leads to an explicit map, whose integrability has been understood by finding two independent integrals of motion and a solution in terms of elliptic functions. Our goal is the construction of its Hamiltonian formulation. After giving a simplified and streamlined presentation of their results, we provide a bi‐Hamiltonian structure for this discretization, thus proving its integrability in the standard Liouville‐Arnold sense (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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