2012/09/30 by Masataka Kanki
Physics and Astronomy · Mathematics · #math-ph #math.DS #math.MP #msc:37K10 #msc:34M55 #msc:37P25
paper · pdf · doi:10.3842/sigma.2013.056
published as SIGMA 9 (2013), 056, 8 pages
arxiv created 2013/09/08 · arxiv updated 2013/09/10
We apply the 'almost good reduction' (AGR) criterion, which has been introduced in our previous (arXiv:1206.4456 and arXiv:1209.0223), to several classes of discrete integrable equations. We verify our conjecture that AGR plays the same role for maps of the plane define over simple finite fields as the notion of the singularity confinement does. We first prove that q-discrete analogues of the Painlevé III and IV equations have AGR. We next prove that the Hietarinta-Viallet equation, a non-integrable chaotic system also has AGR.