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Some recent results on the Kahan-Hirota-Kimura discretization

Quispel, R (La Trobe University)
Friday 12 July 2013, 14:30-15:00

Seminar Room 1, Newton Institute


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.


[pdf ]


This talk has not been recorded due to unpublished work

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