University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > On integrability of the Hirota-Kimura (bilinear) discretizations of integrable quadratic vector fields

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

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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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