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SUMMARY:Admissibility of solutions of discrete dynamical systems - Halburd
 \, R (UCL)
DTSTART:20090514T153000Z
DTEND:20090514T163000Z
UID:TALK18405@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:For discrete equations on a number field\, the rate of growth 
 of the heights of iterates is a good detector of integrability. In the cas
 e of a rational number\, the height is just the maximum of the absolute va
 lue of the denominator and numerator. A solution is called admissible if i
 ts height grows much faster than the heights of the coefficients in the eq
 uation. For certain classes of equations it is shown that the existence of
  a single slow-growing admissible solution is enough to guarantee that the
  equation is a discrete Painleve equation. Inadmissible solutions are also
  explored. These solutions correspond to pre-periodic orbits for classical
  (autonomous) dynamical systems. The classical theory is extended to bette
 r understand these solutions in the non-autonomous setting.
LOCATION:Satellite
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