Integrability of Discrete Equations Modulo a Prime

Integrability of Discrete Equations Modulo a Prime

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 finite fields as the notion...

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Main Author: Masataka Kanki
Format: Article
Language:English
Published: National Academy of Science of Ukraine 2013-09-01
Series:Symmetry, Integrability and Geometry: Methods and Applications
Subjects:
integrability test
good reduction
discrete Painlevé equation
finite field
Online Access:http://dx.doi.org/10.3842/SIGMA.2013.056
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spelling doaj-60e6952dd25943acae61fd08c23743c62020-11-25T00:45:18ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592013-09-01905610.3842/SIGMA.2013.056Integrability of Discrete Equations Modulo a PrimeMasataka KankiWe 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 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.http://dx.doi.org/10.3842/SIGMA.2013.056integrability testgood reductiondiscrete Painlevé equationfinite field
collection DOAJ
language English
format Article
sources DOAJ
author Masataka Kanki
spellingShingle Masataka Kanki
Integrability of Discrete Equations Modulo a Prime
Symmetry, Integrability and Geometry: Methods and Applications
integrability test
good reduction
discrete Painlevé equation
finite field
author_facet Masataka Kanki
author_sort Masataka Kanki
title Integrability of Discrete Equations Modulo a Prime
title_short Integrability of Discrete Equations Modulo a Prime
title_full Integrability of Discrete Equations Modulo a Prime
title_fullStr Integrability of Discrete Equations Modulo a Prime
title_full_unstemmed Integrability of Discrete Equations Modulo a Prime
title_sort integrability of discrete equations modulo a prime
publisher National Academy of Science of Ukraine
series Symmetry, Integrability and Geometry: Methods and Applications
issn 1815-0659
publishDate 2013-09-01
description 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 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.
topic integrability test
good reduction
discrete Painlevé equation
finite field
url http://dx.doi.org/10.3842/SIGMA.2013.056
work_keys_str_mv AT masatakakanki integrabilityofdiscreteequationsmoduloaprime
_version_ 1725270893718929408

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