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Integrability of Discrete Equations Modulo a Prime
Репозиторій DSpace/Manakin
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2013, том 9
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Integrability of Discrete Equations Modulo a Prime
Інший ID:
2010 Mathematics Subject Classification: 37K10; 34M55; 37P25
DOI: http://dx.doi.org/10.3842/SIGMA.2013.056
DOI: http://dx.doi.org/10.3842/SIGMA.2013.056
Посилання:
Integrability of Discrete Equations Modulo a Prime / M. Kanki // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 18 назв. — англ.
Підтримка:
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).
Дата:
2013
Переглядів:
465
Завантажень:
232
Анотація:
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.
