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

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• Suris, YB (Technische Uni Mnchen)
• Tuesday 24 March 2009, 16:30-17:30
• Seminar Room 1 Newton Institute.

If you have a question about this talk, please contact Mustapha Amrani.

Discrete Integrable Systems

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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