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

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)