Far Eastern Mathematical Journal

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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.

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