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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2023, Volume 321, Pages 108–117
DOI: https://doi.org/10.4213/tm4320
(Mi tm4320)
 

This article is cited in 4 scientific papers (total in 4 papers)

The Agrachev–Barilari–Boscain Method and Estimates for the Number of Segments of Horizontal Broken Lines Joining Points in the Canonical Carnot Group $G_{3,3}$

A. V. Greshnov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, pr. Akad. Koptyuga 4, Novosibirsk, 630090 Russia
Full-text PDF (230 kB) Citations (4)
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Abstract: Using a generalization of the Agrachev–Barilari–Boscain method for proving the Rashevskii–Chow theorem, we estimate the minimum number $\mathcal {N}_{G_{3,3}}$ of segments of horizontal broken lines joining two arbitrary points on the six-dimensional two-step canonical Carnot group $G_{3,3}$ with corank $3$ horizontal distribution. We prove that $\mathcal {N}_{G_{3,3}}=3$.
Keywords: canonical Carnot group, Rashevskii–Chow theorem, horizontal broken line.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-281
This work was supported by the Mathematical Center in Akademgorodok (agreement no. 075-15-2022-281 of April 5, 2022, with the Ministry of Science and Higher Education of the Russian Federation).
Received: April 21, 2022
Revised: September 3, 2022
Accepted: January 9, 2023
English version:
Proceedings of the Steklov Institute of Mathematics, 2023, Volume 321, Pages 97–106
DOI: https://doi.org/10.1134/S0081543823020074
Bibliographic databases:
Document Type: Article
UDC: 517.97
Language: Russian
Citation: A. V. Greshnov, “The Agrachev–Barilari–Boscain Method and Estimates for the Number of Segments of Horizontal Broken Lines Joining Points in the Canonical Carnot Group $G_{3,3}$”, Optimal Control and Dynamical Systems, Collected papers. On the occasion of the 95th birthday of Academician Revaz Valerianovich Gamkrelidze, Trudy Mat. Inst. Steklova, 321, Steklov Math. Inst., Moscow, 2023, 108–117; Proc. Steklov Inst. Math., 321 (2023), 97–106
Citation in format AMSBIB
\Bibitem{Gre23}
\by A.~V.~Greshnov
\paper The Agrachev--Barilari--Boscain Method and Estimates for the Number of Segments of Horizontal Broken Lines Joining Points in the Canonical Carnot Group $G_{3,3}$
\inbook Optimal Control and Dynamical Systems
\bookinfo Collected papers. On the occasion of the 95th birthday of Academician Revaz Valerianovich Gamkrelidze
\serial Trudy Mat. Inst. Steklova
\yr 2023
\vol 321
\pages 108--117
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4320}
\crossref{https://doi.org/10.4213/tm4320}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2023
\vol 321
\pages 97--106
\crossref{https://doi.org/10.1134/S0081543823020074}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85171174782}
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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