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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2013 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2013
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149351 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Integrability of Discrete Equations Modulo a Prime / M. Kanki // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 18 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862752072003223552 |
|---|---|
| author | Kanki, M. |
| author_facet | Kanki, M. |
| citation_txt | Integrability of Discrete Equations Modulo a Prime / M. Kanki // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 18 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T21:15:05Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149351 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:15:05Z |
| publishDate | 2013 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kanki, M. 2019-02-21T07:08:28Z 2019-02-21T07:08:28Z 2013 Integrability of Discrete Equations Modulo a Prime / M. Kanki // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 18 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37K10; 34M55; 37P25 DOI: http://dx.doi.org/10.3842/SIGMA.2013.056 https://nasplib.isofts.kiev.ua/handle/123456789/149351 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. The author wish to thank Professors Jun Mada, K.M. Tamizhmani, Tetsuji Tokihiro and Ralph
 Willox for insightful discussions and comments. He also thanks the detailed suggestions by the
 referees. This work is supported by Grant-in-Aid for JSPS Fellows (24-1379). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Integrability of Discrete Equations Modulo a Prime Article published earlier |
| spellingShingle | Integrability of Discrete Equations Modulo a Prime Kanki, M. |
| title | 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_short | Integrability of Discrete Equations Modulo a Prime |
| title_sort | integrability of discrete equations modulo a prime |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149351 |
| work_keys_str_mv | AT kankim integrabilityofdiscreteequationsmoduloaprime |