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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Discretizations of Kahan-Hirota-Kimura type and in
tegrable maps - Hone\, A (Kent)
DTSTART;TZID=Europe/London:20090701T100000
DTEND;TZID=Europe/London:20090701T110000
UID:TALK18957AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/18957
DESCRIPTION:A few years ago\, Hirota and Kimura found a new co
mpletely integrable discretization of the Euler to
p. The method of discretization that they used had
already appeared in the numerical analysis litera
ture\, in the work of Kahan\, who found an unconve
ntional integration scheme for the Lotka-Volterra
predator-prey system. Kahan's approach\, as redisc
overed by Hirota and Kimura\, applies to any syste
m of quadratic vector fields\, and is consistent w
ith a general methodology for nonstandard discreti
zations developed earlier by Mickens. Some new exa
mples of integrable maps have recently been found
using this method. Here we describe the results of
applying this approach to integrable bi-Hamiltoni
an vector fields associated with pairs of compatib
le Lie-Poisson algebras in three dimensions\, and
mention some other examples (including maps from t
he QRT family\, and discrete Painleve equations).
This is joint work with Matteo Petrera and Kim Tow
ler. \n\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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