Integrability of Discrete Equations Modulo a Prime
Mathematical Physics
2013-09-10 v3 Dynamical Systems
math.MP
Abstract
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 Painlev\'e III and IV equations have AGR. We next prove that the Hietarinta-Viallet equation, a non-integrable chaotic system also has AGR.
Keywords
Cite
@article{arxiv.1209.1715,
title = {Integrability of Discrete Equations Modulo a Prime},
author = {Masataka Kanki},
journal= {arXiv preprint arXiv:1209.1715},
year = {2013}
}