Geodesic
Orbital isomorphisms of Liouville systems on a two-dimensional torus
Sbornik. Mathematics, Tome 186 (1995) no. 10, pp. 1531-1549 
E. N. Selivanova. Orbital isomorphisms of Liouville systems on a two-dimensional torus. Sbornik. Mathematics, Tome 186 (1995) no. 10, pp. 1531-1549. http://geodesic.mathdoc.fr/item/SM_1995_186_10_a7/
@article{SM_1995_186_10_a7,
     author = {E. N. Selivanova},
     title = {Orbital isomorphisms of {Liouville} systems on a~two-dimensional torus},
     journal = {Sbornik. Mathematics},
     pages = {1531--1549},
     year = {1995},
     volume = {186},
     number = {10},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_186_10_a7/}
}
TY  - JOUR
AU  - E. N. Selivanova
TI  - Orbital isomorphisms of Liouville systems on a two-dimensional torus
JO  - Sbornik. Mathematics
PY  - 1995
SP  - 1531
EP  - 1549
VL  - 186
IS  - 10
UR  - http://geodesic.mathdoc.fr/item/SM_1995_186_10_a7/
LA  - en
ID  - SM_1995_186_10_a7
ER  - 
%0 Journal Article
%A E. N. Selivanova
%T Orbital isomorphisms of Liouville systems on a two-dimensional torus
%J Sbornik. Mathematics
%D 1995
%P 1531-1549
%V 186
%N 10
%U http://geodesic.mathdoc.fr/item/SM_1995_186_10_a7/
%G en
%F SM_1995_186_10_a7

Voir la notice de l'article provenant de la source Math-Net.Ru

A classification is obtained for geodesic flows of Liouville metrics on a two-dimensional torus up to homeomorphisms preserving the trajectories.

[1] Selivanova E. N., “Klassifikatsiya geodezicheskikh potokov liuvillevykh metrik na dvumernom tore s tochnostyu do topologicheskoi ekvivalentnosti”, Matem. sb., 183:4 (1992), 69–86 | MR

[2] Bolsinov A. V., Fomenko A. T., “Traektornaya ekvivalentnost integriruemykh gamiltonovykh sistem s dvumya stepenyami svobody. Teorema klassifikatsii, I”, Matem. sb., 185:4 (1994), 27–80 | MR | Zbl

[3] Bolsinov A. V., Fomenko A. T., “Traektornaya ekvivalentnost integriruemykh gamiltonovykh sistem s dvumya stepenyami svobody. Teorema klassifikatsii, II”, Matem. sb., 185:5 (1994), 28–78 | MR

[4] Fomenko A. T., “Topologiya poverkhnostei postoyannoi energii integriruemykh gamiltonovykh sistem na trekhmernykh poverkhnostyakh postoyannoi energii”, Izv. AN SSSR. Ser. matem., 50:6 (1986), 1276–1307 | MR | Zbl

[5] Fomenko A. T., Tsishang Kh., “O tipichnykh topologicheskikh svoistvakh integriruemykh gamiltonovykh sistem”, Izv. AN SSSR. Ser. matem., 52:2 (1988), 378–407 | MR | Zbl

[6] Bolsinov A. V., Matveev S. V., Fomenko A. T., “Topologicheskaya klassifikatsiya integriruemykh gamiltonovykh sistem s dvumya stepenyami svobody. Spisok sistem maloi slozhnosti”, UMN, 45:2 (1990), 49–77 | MR

[7] Dini U., “Sopra un problema che si presenta nella theoria generale delle rappresetazioni geografice di una superficie su di un'altra”, Ann. di Math. Ser. 2, 3 (1869), 269–293

[8] Darboux G., Lecons sur la théorie generale des surfaces et les applications géometriques du calcul infenitesimal, Gautier-Villar, Paris, 1891

[9] Raffy M. L., “Determination des éléments linéaires doublement harmoniques”, J. de Math. Ser. 4, 2 (1894)

[10] Levi-Chivita T., “Sulle transformazioni della equazioni dinamiche”, Ann. di Math., 2:24 (1896)

[11] Birkgof Dzh. D., Dinamicheskie sistemy, OGIZ, M.–L., 1941

[12] Krasnov M. L., Integralnye uravneniya. Vvedenie v teoriyu, Nauka, M., 1975 | MR | Zbl