Geodesic
On Growth Function of $n$-Valued Dynamics
Matematičeskie zametki, Tome 115 (2024) no. 3, pp. 458-465 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper answers the question of V. M. Buchstaber on growth function in case of certain $n$-valued group. This question is in close relation to specific discrete integrable systems. In this paper we find a specific formula for growth function given the case of prime $n$. We also prove a polynomial asymptotic estimate of the growth function in general case. At the end we pose new conjectures and questions regarding growth functions.
Keywords: $n$-valued group, $n$-valued dynamics, growth function
Mots-clés : cyclic composition. 
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M. A. Chirkov. On Growth Function of $n$-Valued Dynamics. Matematičeskie zametki, Tome 115 (2024) no. 3, pp. 458-465. http://geodesic.mathdoc.fr/item/MZM_2024_115_3_a11/

[1] V. M. Bukhshtaber, S. P. Novikov, “Formalnye gruppy, stepennye sistemy i operatory Adamsa”, Matem. sb., 84 (126):1 (1971), 81–118 | MR | Zbl

[2] V. M. Bukhshtaber, “Funktsionalnye uravneniya, assotsiirovannye s teoremami slozheniya dlya ellipticheskikh funktsii, i dvuznachnye algebraicheskie gruppy”, UMN, 45:3 (273) (1990), 185–186 | MR | Zbl

[3] V. M. Bukhshtaber, E. G. Ris, “Koltsa nepreryvnykh funktsii, simmetricheskie proizvedeniya i algebry Frobeniusa”, UMN, 59:1 (355) (2004), 125–144 | DOI | MR | Zbl

[4] “$n$-valued groups: theory and applications”, Mosc. Math. J., 6:1 (2006), 57–84 | DOI | MR | Zbl

[5] A. P. Veselov, “Integriruemye otobrazheniya”, UMN, 46:5 (281) (1991), 3–45 | MR | Zbl

[6] V. M. Buchstaber, A. P. Veselov, “Integrable correspondences and algebraic representations of multivalued groups”, Internat. Math. Res. Notices, 1996, no. 8, 381–400 | DOI | MR

[7] A. P. Veselov, “O roste chisla obrazov tochki pri iteratsiyakh mnogoznachnogo otobrazheniya”, Matem. zametki, 49:2 (1991), 29–35 | MR | Zbl

[8] V. M. Bukhshtaber, A. P. Veselov, “Topograf Konveya, $\mathrm{PGL}_2(\mathbb Z)$-dinamika i dvuznachnye gruppy”, UMN, 74:3 (447) (2019), 17–62 | DOI | MR | Zbl

[9] V. M. Buchstaber, V. I. Dragovich, “Two-valued groups, Kummer varieties, and integrable billiards”, Arnold Math. J., 4:1 (2018), 27–57 | DOI | MR

[10] A. Knopfmacher, N. Robbins, “Some properties of cyclic compositions”, Fibonacci Quart., 48:3 (2010), 249–255 | MR

[11] K. Ireland, M. Rosen, A Classical Introduction to Modern Number Theory, Grad. Texts in Math., 84, Springer, New York, 1982 | MR

[12] V. V. Prasolov, Mnogochleny, MTsNMO, M., 2003 | MR