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Some recent results on the Kahan-Hirota-Kimura discretization

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

Discrete Integrable Systems

We show that Kahan’s discretization of quadratic vector fields is equivalent to a Runge- Kutta method. In case the vector field is Hamiltonian, with constant Poisson structure, the map determined by this discretization preserves a (modified) integral and a (modified) invariant measure. This produces large classes of integrable rational mappings, explaining some of the integrable cases that were previously known, as well as yielding many new ones.

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

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