This article is cited in 3 papers

Integrability of Discrete Equations Modulo a Prime

Masataka Kanki

Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Tokyo 153-8914, Japan

Abstract: We apply the “almost good reduction” (AGR) criterion, which has been introduced in our previous works, 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 fiinite 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.

Keywords: integrability test; good reduction; discrete Painlevé equation; finite field.

MSC: 37K10; 34M55; 37P25

Received: April 24, 2013; in final form September 5, 2013

Language: English

DOI: 10.3842/SIGMA.2013.056

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ArXiv: 1209.1715