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 Mat. Sb., 2018, Volume 209, Number 6, Pages 65–74 (Mi msb8852)

Galois theory, the classification of finite simple groups and a dense winding of a torus

D. D. Kiselev

Abstract: The Galois group of the Zelikin-Lokutsievskii polynomial is studied. It is established that, in the generalized Fuller problem, for any positive integer $k\leqslant 249 994 914$ there is an optimal control going along a dense winding of the $k$-dimensional torus in finite time. In the generalized Fuller problem, under the assumption that the Zelikin-Lokutsievskiy polynomials are irreducible over the field of rational numbers for almost all prime powers it is shown that there is an optimal control passing along a dense winding of the torus of any preassigned dimension in finite time. Many examples are considered.
Bibliography: 7 titles.

Keywords: optimal control, dense winding, Galois group, classification of finite simple groups, Wolstenholme primes.

DOI: https://doi.org/10.4213/sm8852

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English version:
Sbornik: Mathematics, 2018, 209:6, 840–849

Bibliographic databases:

UDC: 512.623.3+512.622+517.977.5
MSC: Primary 11R09, 11R32; Secondary 49K15

Citation: D. D. Kiselev, “Galois theory, the classification of finite simple groups and a dense winding of a torus”, Mat. Sb., 209:6 (2018), 65–74; Sb. Math., 209:6 (2018), 840–849

Citation in format AMSBIB
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