Integrability of Discrete Equations Modulo a Prime

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 Painlevé III and IV equations have AGR. We next prove that the Hietarinta-Viallet equation, a non-integrable chaotic system also has AGR.

References in corpus (2)

• Discrete Painleve II equation over finite fields
• The space of initial conditions and the property of an almost good reduction in discrete Painleve II equations over finite fields

Cited by in corpus (5)

• Some integrable maps and their Hirota bilinear forms
• Singularities of the discrete KdV equation and the Laurent property
• Studies on the discrete integrable equations over finite fields
• The space of initial conditions and the property of an almost good reduction in discrete Painleve II equations over finite fields
• Discrete Painleve equations and discrete KdV equation over finite fields