Trudy Matematicheskogo Instituta imeni V.A. Steklova
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy Mat. Inst. Steklova:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2023, Volume 321, Pages 252–285
DOI: https://doi.org/10.4213/tm4318
(Mi tm4318)
 

Abnormal Trajectories in the Sub-Riemannian $(2,3,5,8)$ Problem

Yu. L. Sachkov, E. F. Sachkova

Ailamazyan Program Systems Institute of Russian Academy of Sciences, Pereslavl-Zalessky, Yaroslavl Region, 152021 Russia
References:
Abstract: Abnormal trajectories are of particular interest for sub-Riemannian geometry, because the most complicated singularities of the sub-Riemannian metric are located just near such trajectories. Important open questions in sub-Riemannian geometry are to establish whether the abnormal length minimizers are smooth and to describe the set filled with abnormal trajectories starting from a fixed point. For example, the Sard conjecture in sub-Riemannian geometry states that this set has measure zero. In this paper, we consider this and other related properties of such a set for the left-invariant sub-Riemannian problem with growth vector $(2,3,5,8)$. We also study the global and local optimality of abnormal trajectories and obtain their explicit parametrization.
Keywords: sub-Riemannian geometry, abnormal trajectories, abnormal set, local and global optimality.
Funding agency Grant number
Russian Science Foundation 22-11-00140
This work was supported by the Russian Science Foundation under grant no. 22-11-00140, https://rscf.ru/en/project/22-11-00140/.
Received: June 10, 2022
Revised: July 29, 2022
Accepted: February 22, 2023
English version:
Proceedings of the Steklov Institute of Mathematics, 2023, Volume 321, Pages 236–268
DOI: https://doi.org/10.1134/S0081543823020177
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: Yu. L. Sachkov, E. F. Sachkova, “Abnormal Trajectories in the Sub-Riemannian $(2,3,5,8)$ Problem”, 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, 252–285; Proc. Steklov Inst. Math., 321 (2023), 236–268
Citation in format AMSBIB
\Bibitem{SacSac23}
\by Yu.~L.~Sachkov, E.~F.~Sachkova
\paper Abnormal Trajectories in the Sub-Riemannian $(2,3,5,8)$ Problem
\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 252--285
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4318}
\crossref{https://doi.org/10.4213/tm4318}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4643645}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2023
\vol 321
\pages 236--268
\crossref{https://doi.org/10.1134/S0081543823020177}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85170849319}
Linking options:
  • https://www.mathnet.ru/eng/tm4318
  • https://doi.org/10.4213/tm4318
  • https://www.mathnet.ru/eng/tm/v321/p252
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
    Statistics & downloads:
    Abstract page:120
    Full-text PDF :11
    References:18
    First page:1
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024