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Sbornik: Mathematics, 2020, Volume 211, Issue 10, Pages 1460–1485
DOI: https://doi.org/10.1070/SM9266 (Mi sm9266) 		 
This article is cited in 9 scientific papers (total in 9 papers)

The structure of abnormal extremals in a sub-Riemannian problem with growth vector $(2, 3, 5, 8)$

Yu. L. Sachkovab, E. F. Sachkovaab

a Ailamazyan Program Systems Institute of Russian Academy of Sciences, Ves’kovo, Pereslavl’ district, Yaroslavl’ oblast’, Russia
b University of Science and Technology "Sirius", Sochi, Russia
English version PDF (693 kB) Citations (9)
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DOI: https://doi.org/10.1070/SM9266
Abstract: A left-invariant sub-Riemannian problem on a free nilpotent Lie group of step 4 with two generators is considered. The structure of abnormal extremals is described. These extremals are shown to define an abnormal foliation of the annihilator of the square of the distribution, which is given by the intersections of this annihilator with the leaves of the symplectic foliation of the Lie coalgebra. The question of abnormal trajectories being strictly/nonstrictly abnormal is investigated, their projection onto a plane of the distribution are described, estimates for the corank are given and examples of nonsmooth trajectories are constructed.
Bibliography: 14 titles.
Keywords: sub-Riemannian problem, abnormal extremals, abnormal trajectories, strict/nonstrict abnormality.
Funding agency Grant number
Russian Science Foundation 17-11-01387-П
Russian Foundation for Basic Research 19-31-51023
The work in §§ 2–4 was supported by the Russian Science Foundation under grant no. 17-11-01387-П and carried out in the Ailamazyan Program Systems Institute of the Russian Academy of Sciences. The work in §§ 5–7 was supported by the Russian Foundation for Basic Research (grant no. 19-31-51023) and carried out in the University of Science and Technology “Sirius”.
Received: 18.04.2019 and 20.04.2020
Russian version:
Matematicheskii Sbornik, 2020, Volume 211, Number 10, Pages 112–138
DOI: https://doi.org/10.4213/sm9266
Bibliographic databases:
Document Type: Article
UDC: 517.977
MSC: Primary 53C17; Secondary 22E25, 49K15
Language: English
Original paper language: Russian
Citation: Yu. L. Sachkov, E. F. Sachkova, “The structure of abnormal extremals in a sub-Riemannian problem with growth vector $(2, 3, 5, 8)$”, Mat. Sb., 211:10 (2020), 112–138; Sb. Math., 211:10 (2020), 1460–1485
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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