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

Matteo Petrera, Yuri B. Suris

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

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.

Original languageEnglish
Pages (from-to)1654-1663
Number of pages10
JournalMathematische Nachrichten
Volume283
Issue number11
DOIs
StatePublished - Nov 2010
Externally publishedYes

Keywords

  • Euler top
  • Integrable discretization

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