FAR EASTERN BRANCH OF THE RUSSIAN ACADEMY OF SCIENCES
INSTITUTE OF APPLIED MATHEMATICS KHABAROVSK DIVISION
Far Eastern Mathematical Journal
Periodic ultradiscrete transformations of the plane with periods of 5, 7, 8, 9 |
Avdeeva M.O. |
2021, issue 2, P. 127–132 DOI: https://doi.org/10.47910/FEMJ202111 |
Abstract |
| V.A. Bykovskii constructed three new periodic ultradiscrete transformations of the plane In addition to the two well-known. In his work, only the idea of proving these statements was proposed. We give a complete and detailed proof of them for sequences with periods 5, 7, 8, 9. |
Keywords: nonlinear recurrent sequences, tropical sequences, nonlinear periodic transformations |
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References |
| [1] A. Nobe, “Ultradiscrete QRT maps and tropical elliptic curves”, J.Journal of Physics A: Mathematical and Theoretical, 41:12. 125205 (2008), 12 pp. [2] V.A. Bykovskii, “Periodicheskie ul'tradiskretnye preobrazovaniia ploskosti”, Doklady Rossiiskoi akademii nauk. Matematika, informatika, protsessy upravleniia, 500 (2021), 23–25. [3] A.P. Fordy, A. Hone, “Symplectic Maps from Cluster Algebras”, SIGMA, 7.091 (2011), 1–12. |