Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2016, Number 1, Pages 40–44 (Mi vmumm120)  
This article is cited in 3 scientific papers (total in 3 papers)

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The Bertrand’s manifolds with equators

E. A. Kudryavtseva, D. A. Fedoseev

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (318 kB) Citations (3)
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Abstract: Natural mechanical systems describing the motion of a particle on a two-dimensional Riemannian manifold of revolution in the field of a central smooth potential are studied in the paper. A complete classification of such Riemannian manifolds and potentials on them possessing the strengthened Bertrand property, i.e., any orbit not contained in any meridian is closed, is obtained.
Key words: Bertrand's Riemannian manifold, surface of revolution, equator, Tannery's manifold, the Maupertuis principle.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-00664-а
Ministry of Education and Science of the Russian Federation НШ-1410.2012.1
Received: 24.06.2014
English version:
Moscow University Mathematics Bulletin, 2016, Volume 71, Issue 1, Pages 23–26
DOI: https://doi.org/10.3103/S0027132216010046
Bibliographic databases:
Document Type: Article
UDC: 514.853
Language: Russian
Citation: E. A. Kudryavtseva, D. A. Fedoseev, “The Bertrand’s manifolds with equators”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2016, no. 1, 40–44; Moscow University Mathematics Bulletin, 71:1 (2016), 23–26
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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