Geodesic
Galois theory, the classification of finite simple groups and a dense winding of a torus
Sbornik. Mathematics, Tome 209 (2018) no. 6, pp. 840-849 Cet article a éte moissonné depuis la source Math-Net.Ru

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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, classification of finite simple groups, Wolstenholme primes.
Mots-clés : Galois group 
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D. D. Kiselev. Galois theory, the classification of finite simple groups and a dense winding of a torus. Sbornik. Mathematics, Tome 209 (2018) no. 6, pp. 840-849. http://geodesic.mathdoc.fr/item/SM_2018_209_6_a3/

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