Sbornik: Mathematics
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
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






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


Sbornik: Mathematics, 2006, Volume 197, Issue 6, Pages 901–950
DOI: https://doi.org/10.1070/SM2006v197n06ABEH003783
(Mi sm1572)
 

This article is cited in 41 scientific papers (total in 41 papers)

Complete description of the Maxwell strata in the generalized Dido problem

Yu. L. Sachkov

Program Systems Institute of RAS
References:
Abstract: The generalized Dido problem is considered – a model of the nilpotent sub-Riemannian problem with the growth vector $(2,3,5)$. The Maxwell set is studied, that is, the locus of the intersection points of geodesics of equal length. A complete description is obtained for the Maxwell strata corresponding to the symmetry group of the exponential map generated by rotations and reflections. All the corresponding Maxwell times are found and located. The conjugate points that are limit points of the Maxwell set are also found. An upper estimate is obtained for the cut time (time of loss of optimality) on geodesics.
Bibliography: 12 titles.
Received: 29.03.2005
Russian version:
Matematicheskii Sbornik, 2006, Volume 197, Number 6, Pages 111–160
DOI: https://doi.org/10.4213/sm1572
Bibliographic databases:
UDC: 517.977
MSC: Primary 53C17; Secondary 17B66, 49J15, 53C22, 93C15
Language: English
Original paper language: Russian
Citation: Yu. L. Sachkov, “Complete description of the Maxwell strata in the generalized Dido problem”, Sb. Math., 197:6 (2006), 901–950
Citation in format AMSBIB
\Bibitem{Sac06}
\by Yu.~L.~Sachkov
\paper Complete description of the Maxwell strata in the
generalized Dido problem
\jour Sb. Math.
\yr 2006
\vol 197
\issue 6
\pages 901--950
\mathnet{http://mi.mathnet.ru//eng/sm1572}
\crossref{https://doi.org/10.1070/SM2006v197n06ABEH003783}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2477284}
\zmath{https://zbmath.org/?q=an:1148.53022}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000240354900011}
\elib{https://elibrary.ru/item.asp?id=17309850}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33748799482}
Linking options:
  • https://www.mathnet.ru/eng/sm1572
  • https://doi.org/10.1070/SM2006v197n06ABEH003783
  • https://www.mathnet.ru/eng/sm/v197/i6/p111
  • This publication is cited in the following 41 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:641
    Russian version PDF:273
    English version PDF:27
    References:74
    First page:1
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024