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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”, Mat. Sb., 197:6 (2006), 111–160; Sb. Math., 197:6 (2006), 901–950
Citation in format AMSBIB
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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
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    Abstract page:637
    Russian version PDF:272
    English version PDF:26
    References:72
    First page:1
     
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