1209.1715 (Masataka Kanki)

Integrability of discrete equations modulo a prime    [PDF]

Masataka Kanki

We apply the `almost good reduction' (AGR) criterion, which has been introduced in our previous works (letter arXiv:1206.4456 and full paper arXiv:1209.0223), to several classes of discrete integrable equations. We first verify our conjecture that AGR can be used as a criterion for integrability of dynamical systems over finite fields, by proving that several q-discrete Painleve equations have AGR. We then discuss the reduction of a chaotic discrete system and state that AGR is essentially an arithmetic analogue of the singularity confinement method. Keywords: Integrability test, Good reduction, Discrete Painleve equation, Finite field.

View original: http://arxiv.org/abs/1209.1715