Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2017, Number 3, Pages 35–43 (Mi vmumm67)  
This article is cited in 4 scientific papers (total in 4 papers)

Mathematics

Liouville classification of integrable geodesic flows on a torus of revolution in a potential field

D. S. Timonina

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (511 kB) Citations (4)
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Abstract: A Liouville classification of integrable Hamiltonian systems being geodesic flows on a 2-dimensional torus of revolution in an invariant potential field in the case of linear integral is obtained. This classification is obtained using the Fomenko–Zieschang invariant (marked molecules) of studied systems. All types of bifurcation curves are described. A classification of singularities of the system solutions is also obtained.
Key words: integrable Hamiltonian systems, geodesic flow, surfaces of revolution, Fomenko–Zieschang invariant, torus.
Received: 09.11.2016
English version:
Moscow University Mathematics Bulletin, 2017, Volume 72, Issue 3, Pages 121–128
DOI: https://doi.org/10.3103/S0027132217030056
Bibliographic databases:
Document Type: Article
UDC: 514.7, 514.8
Language: Russian
Citation: D. S. Timonina, “Liouville classification of integrable geodesic flows on a torus of revolution in a potential field”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2017, no. 3, 35–43; Moscow University Mathematics Bulletin, 72:3 (2017), 121–128
Citation in format AMSBIB
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