Loading [MathJax]/jax/output/CommonHTML/jax.js
Program Systems: Theory and Applications
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Program Systems: Theory and Applications:
Year:
Volume:
Issue:
Page:
Find






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


Program Systems: Theory and Applications, 2015, Volume 6, Issue 2, Pages 45–61 (Mi ps168)  

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

Optimization Methods and Control Theory

On the free Carnot (2,3,5,8) group

J.-P. Gauthiera, Yu. L. Sachkovb

a Laboratoire des Sciences de l’Information et des Systèmes, UMR, CNRS, France
b Ailamazyan Program System Institute of RAS
References:
Abstract: We consider the free nilpotent Lie algebra L with 2 generators, of step 4, and the corresponding connected simply connected Lie group G, with the aim to study the left-invariant sub-Riemannian structure on G defined by the generators of L as an orthonormal frame.
We compute two vector field models of L by polynomial vector fields in R8, and find an infinitesimal symmetry of the sub-Riemannian structure. Further, we compute explicitly the product rule in G and the right-invariant frame on G.
Key words and phrases: sub-Riemannian geometry, Carnot group.
Received: 26.04.2015
Accepted: 20.05.2015
Document Type: Article
UDC: 517.977
MSC: 53C17
Language: English
Citation: J.-P. Gauthier, Yu. L. Sachkov, “On the free Carnot (2,3,5,8) group”, Program Systems: Theory and Applications, 6:2 (2015), 45–61
Citation in format AMSBIB
\Bibitem{GauSac15}
\by J.-P.~Gauthier, Yu.~L.~Sachkov
\paper On the free Carnot (2,3,5,8) group
\jour Program Systems: Theory and Applications
\yr 2015
\vol 6
\issue 2
\pages 45--61
\mathnet{http://mi.mathnet.ru/ps168}
Linking options:
  • https://www.mathnet.ru/eng/ps168
  • https://www.mathnet.ru/eng/ps/v6/i2/p45
  • This publication is cited in the following 4 articles:
    1. Yu. L. Sachkov, E. F. Sachkova, “The structure of abnormal extremals in a sub-Riemannian problem with growth vector $(2, 3, 5, 8)$”, Sb. Math., 211:10 (2020), 1460–1485  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Yu. L. Sachkov, E. F. Sachkova, “Symmetries and Parameterization of Abnormal Extremals in the Sub-Riemannian Problem with the Growth Vector (2, 3, 5, 8)”, Rus. J. Nonlin. Dyn., 15:4 (2019), 577–585  mathnet  crossref  elib
    3. L. V. Lokutsievskiy, Yu. L. Sachkov, “Liouville integrability of sub-Riemannian problems on Carnot groups of step 4 or greater”, Sb. Math., 209:5 (2018), 672–713  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. D. I. Pirshtuk, “O kharakteristicheskikh raspredeleniyakh levoinvariantnykh zadach optimalnogo upravleniya”, Tr. In-ta matem., 25:2 (2017), 70–81  mathnet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Program Systems: Theory and Applications
    Statistics & downloads:
    Abstract page:310
    Full-text PDF :114
    References:52
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025