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Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2015, Number 1, Pages 62–65 (Mi vmumm211)  

This article is cited in 1 scientific paper (total in 1 paper)

Short notes

Bifurcation diagrams of natural Hamiltonian systems on Bertrand manifolds

D. A. Fedoseev

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Bifurcation diagrams for natural integrable Hamiltonian systems on Bertrand manifolds (i.e., on configuration spaces of one inverse problem of dynamics) are constructed. Some properties of the corresponding Liuoville foliations are studied, namely, the compactness and the number of foliation components in the preimage under momentum map.

Key words: Bertrand's Riemannian manifold, surface of revolution, Hamiltonian systems, bifurcation diagram.

Funding Agency Grant Number
Government of the Russian Federation 11.G34.31.0054
Russian Foundation for Basic Research 13-01-00664-а
Ministry of Education and Science of the Russian Federation НШ-1410.2012.1


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English version:
Moscow University Mathematics Bulletin, 2015, 70:1, 44–47

Bibliographic databases:

UDC: 511
Received: 22.01.2014

Citation: D. A. Fedoseev, “Bifurcation diagrams of natural Hamiltonian systems on Bertrand manifolds”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2015, no. 1, 62–65; Moscow University Mathematics Bulletin, 70:1 (2015), 44–47

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. A. Fedoseev, A. T. Fomenko, “Nekompaktnye osobennosti integriruemykh dinamicheskikh sistem”, Fundament. i prikl. matem., 21:6 (2016), 217–243  mathnet
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