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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
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
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
Linking options:
https://www.mathnet.ru/eng/sm1572https://doi.org/10.1070/SM2006v197n06ABEH003783 https://www.mathnet.ru/eng/sm/v197/i6/p111
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Abstract page: | 637 | Russian version PDF: | 272 | English version PDF: | 26 | References: | 72 | First page: | 1 |
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