### On integrability of the Hirota-Kimura (bilinear) discretizations of integrable quadratic vector fields

Suris, YB *(Technische Uni München)*

Tuesday 24 March 2009, 16:30-17:30

Meeting Room 3, CMS

#### Abstract

R. Hirota and K. Kimura discovered integrable discretizations of the Euler and the Lagrange tops, given by birational maps. Their method is a specialization to the integrable context of a general discretization scheme introduced by W. Kahan and applicable to any vector field with a quadratic dependence on phase variables.
Discretizations of the Hirota-Kimura type can be considered for numerous integrable systems of classical mechanics. Due to a remarkable and not well understood mechanism, such discretizations seem to inherit the integrability for most of (if not all) algebraically completely integrable systems. We will discuss in detail the Hirota-Kimura discretization of the Clebsch system and of the so(4) Euler top.

#### Presentation