FAR EASTERN BRANCH OF THE RUSSIAN ACADEMY OF SCIENCES
INSTITUTE OF APPLIED MATHEMATICS KHABAROVSK DIVISION
Far Eastern Mathematical Journal
Periodic ultradiscrete plane transformation with a period of 12 |
Monina M.D. |
2021, issue 2, P. 231–233 DOI: https://doi.org/10.47910/FEMJ202119 |
Abstract |
| V.A. Bykovskii constructed a new periodic ultradiscrete plane transformation with a period of 12. In his work only the idea of proving this periodicity was proposed. We provide a complete and detailed proof of this statement. |
Keywords: nonlinear recurrent sequences, tropical sequences, nonlinear periodic transformations |
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References |
| [1] V.A. Bykovskii, “Periodicheskie ul'tradispersnye preobrazovaniia ploskosti”, Doklady Rossiiskoi akademii nauk. Matematika, informatika, protsessy upravleniia, 500 (2021), 53–55. [2] A. Nobe, “Ultradiscrete QRT maps and tropical elliptic curves”, J. Journal of Physics A: Mathematical and Theoretical, 41:12 (2008), 12 pp. [3] D. Takahashi, J. Satsuma, “A Soliton Cellular Automaton”, Journal of the Physical Society of Japan, 59:10 (1990), 3514–3519. [4] J. Matsukidaira, J. Satsuma, D. Takahashi, T. Tokihiro, M. Torii, “Toda-type cellular automaton and its N-soliton solution”, Physics Letters A, 225:4–6 (1997), 287–295. [5] Chris Ormerod, An ultradiscrete QRT mapping from tropical elliptic curves, arXiv:math-ph/0609060v1, 22 Sep 2006. |