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SUMMARY:Integrability of discrete systems over finite fields - Kanki\, M (
 University of Tokyo)
DTSTART:20130711T090000Z
DTEND:20130711T093000Z
UID:TALK46189@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Discrete integrable systems defined over finite fields are stu
 died. Dynamical systems over\nnon-Archimedean fields are of great interest
  in the theory of arithmetic dynamical systems [1].Discrete integrable equ
 ations over the field of p -adic numbers are defined and then the evolutio
 ns are reduced to the finite field. The integrable systems are shown to ha
 ve a property that resembles a 'good reduction' modulo a prime [2]. We obs
 erve that this generalization of the good reduction can be used to test in
 tegrability of discrete equations over finite fields. We discuss the relat
 ion of our methods to other integrability tests\, in particular\, the 'sin
 gularity confinement test'. \nApplications of our approach to the two-dime
 nsional lattice systems such as the discrete\nKdV equation are also studie
 d.\n\n[1] J. H. Silverman\, The Arithmetic of Dynamical Systems\, (2007)\,
  Springer-Verlag\, New\nYork.\n[2] M. Kanki\, J. Mada\, K. M. Tamizhmani\,
  T. Tokihiro\, Discrete Painleve II equation over\nfinite fields\, J. Phy
 s. A: Math. Theor.\, 45\, (2012)\, 342001 (8pp).\n
LOCATION:Seminar Room 1\, Newton Institute
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