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SUMMARY:Discretizations of Kahan-Hirota-Kimura type and integrable maps - 
 Hone\, A (Kent)
DTSTART:20090701T090000Z
DTEND:20090701T100000Z
UID:TALK18957@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:A few years ago\, Hirota and Kimura found a new completely int
 egrable discretization of the Euler top. The method of discretization that
  they used had already appeared in the numerical analysis literature\, in 
 the work of Kahan\, who found an unconventional integration scheme for the
  Lotka-Volterra predator-prey system. Kahan's approach\, as rediscovered b
 y Hirota and Kimura\, applies to any system of quadratic vector fields\, a
 nd is consistent with a general methodology for nonstandard discretization
 s developed earlier by Mickens. Some new examples of integrable maps have 
 recently been found using this method. Here we describe the results of app
 lying this approach to integrable bi-Hamiltonian vector fields associated 
 with pairs of compatible Lie-Poisson algebras in three dimensions\, and me
 ntion some other examples (including maps from the QRT family\, and discre
 te Painleve equations). This is joint work with Matteo Petrera and Kim Tow
 ler. \n\n
LOCATION:Seminar Room 1\, Newton Institute
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