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Mat. Sb., 2016, Volume 207, Number 4, Pages 113–122 (Mi msb8471)  

This article is cited in 1 scientific paper (total in 1 paper)

On a dense winding of the 2-dimensional torus

D. D. Kiselev

All-Russian Academy of International Trade, Moscow

Abstract: An important role in the solution of a class of optimal control problems is played by a certain polynomial of degree $2(n-1)$ of special form with integer coefficients. The linear independence of a family of $k$ special roots of this polynomial over $\mathbb{Q}$ implies the existence of a solution of the original problem with optimal control in the form of a dense winding of a $k$-dimensional Clifford torus, which is traversed in finite time. In this paper, it is proved that for every integer $n>3$ one can take $k$ to be equal to $2$.
Bibliography: 6 titles.

Keywords: optimal control, dense winding, Galois group, linear independence.

DOI: https://doi.org/10.4213/sm8471

Full text: PDF file (474 kB)
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English version:
Sbornik: Mathematics, 2016, 207:4, 581–589

Bibliographic databases:

Document Type: Book
UDC: 512.623.3+512.622+517.977.5
MSC: Primary 49K15; Secondary 49N10, 93B50
Received: 09.01.2015 and 09.10.2015

Citation: D. D. Kiselev, “On a dense winding of the 2-dimensional torus”, Mat. Sb., 207:4 (2016), 113–122; Sb. Math., 207:4 (2016), 581–589

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm8471
  • http://mi.mathnet.ru/eng/msb/v207/i4/p113

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. D. Kiselev, “Galois theory, the classification of finite simple groups and a dense winding of a torus”, Sb. Math., 209:6 (2018), 840–849  mathnet  crossref  crossref  adsnasa  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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