Geodesic
On~typical topological properties of integrable Hamiltonian systems
Izvestiya. Mathematics , Tome 32 (1989) no. 2, pp. 385-412.

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

The typical properties of integrable Hamiltonian systems in “general position” are described, along with the topology of constant-energy surfaces of such systems. It is proved that in the “typical case” all stable periodic solutions of the system are not contractible and are pairwise not homotopic. Bibliography: 25 titles. 
@article{IM2_1989_32_2_a6,
     author = {A. T. Fomenko and H. Zieschang},
     title = {On~typical topological properties of integrable {Hamiltonian} systems},
     journal = {Izvestiya. Mathematics },
     pages = {385--412},
     publisher = {mathdoc},
     volume = {32},
     number = {2},
     year = {1989},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1989_32_2_a6/}
}
TY  - JOUR
AU  - A. T. Fomenko
AU  - H. Zieschang
TI  - On~typical topological properties of integrable Hamiltonian systems
JO  - Izvestiya. Mathematics 
PY  - 1989
SP  - 385
EP  - 412
VL  - 32
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1989_32_2_a6/
LA  - en
ID  - IM2_1989_32_2_a6
ER  - 
%0 Journal Article
%A A. T. Fomenko
%A H. Zieschang
%T On~typical topological properties of integrable Hamiltonian systems
%J Izvestiya. Mathematics 
%D 1989
%P 385-412
%V 32
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1989_32_2_a6/
%G en
%F IM2_1989_32_2_a6
A. T. Fomenko; H. Zieschang. On~typical topological properties of integrable Hamiltonian systems. Izvestiya. Mathematics , Tome 32 (1989) no. 2, pp. 385-412. http://geodesic.mathdoc.fr/item/IM2_1989_32_2_a6/

[1] Fomenko A. T., “Topologiya poverkhnostei postoyannoi energii integriruemykh sistem i prepyatstviya k integriruemosti”, Izv. AN SSSR. Ser. matem., 50:6 (1986), 1276–1307 | MR | Zbl

[2] Fomenko A. T., “Topologiya trekhmernykh mnogoobrazii i integriruemye mekhanicheskie sistemy”, V Tiraspolskii simpozium po obschei topologii i ee prilozheniyam, Kishinev, 1985, 235–237

[3] Fomenko A. T., “Teoriya Morsa integriruemykh gamiltonovykh sistem”, Dokl. AN SSSR, 287:5 (1986), 1071–1075 | MR | Zbl

[4] Arnold V. I., Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1974 | MR

[5] Novikov S. P., “Variatsionnye metody i periodicheskie resheniya uravnenii tipa Kirkhgofa, II”, Funkts. analiz i ego prilozh., 15:4 (1981), 37–52 | MR

[6] Trofimov V. V., Fomenko A. T., “Integriruemost po Liuvillyu gamiltonovykh sistem na algebrakh Li”, UMN, 39:2 (1984), 3–56 | MR | Zbl

[7] Orlik P., Vogt E., Zieschang H., “Zur Topologie gefaserter dreidimensionaler Mannigfaltigkeiten”, Topology, 6:1 (1967), 49–65 | DOI | MR

[8] Bogoyavlenskii O. I., Ivakh G. F., “Topologicheskii analiz integriruemykh sluchaev B. A. Steklova”, UMN, 40:4 (1985), 145–146 | MR | Zbl

[9] Brailov A. V., “Polnaya integriruemost nekotorykh geodezicheskikh potokov i integriruemye sistemy s nekommutiruyuschimi integralami”, Dokl. AN SSSR, 271:2 (1983), 273–276 | MR

[10] Waldhausen F., “Eine Klasse von $3$-dimensionalen Mannigfaltigkeiten, I, II”, Invent. Math., 3:4 (1967), 308–333 | DOI | MR | Zbl

[11] Morgan J. W., “Non-singular Morse–Smale flows on $3$-dimensional manifolds”, Topology, 18:1 (1979), 41–53 | DOI | MR | Zbl

[12] Asimov D., “Round handles and non-singular Morse–Smale flows”, Ann. of Math., 102:1 (1975), 41–54 | DOI | MR | Zbl

[13] Thurston W., “Existence of codimension – one foliations”, Ann. of Math., 104:2 (1976), 249–268 | DOI | MR | Zbl

[14] Miyoshi S., “Foliated round surgery of codimension-one foliated manifolds”, Topology, 21 (1982), 245–262 | DOI | MR

[15] Anosov D. V., “O tipichnykh svoistvakh zamknutykh geodezicheskikh”, Izv. AN SSSR. Ser. matem., 46:4 (1982), 675–709 | MR | Zbl

[16] Kozlov V. V., “Integriruemost i neintegriruemost v gamiltonovoi mekhanike”, UMN, 38:1 (1983), 3–67 | MR | Zbl

[17] Burmistrova A. B., Matveev S. V., “Struktura funktsii na orientiruemykh 3-mnogoobraziyakh”, Tezisy XI Vsesoyuznoi shkoly po teorii operatorov v funktsionalnykh prostranstvakh, Tez. dokl., Chelyabinsk, 1986, 12

[18] Hempel J., 3-manifolds, Annals of Math. Studies, 86, Princeton Univ. Press, Princeton, 1976 | MR | Zbl

[19] Lyndon R., Schupp P., Combinatorial group theory, Springer-Verlag, Berlin, Heidelberg, New York, 1977 | MR | Zbl

[20] Zieschang H., Vogt E., Coldeway H. D., Surfaces and planar discontinuous groups, Lect. Notes in Math., 835, Springer-Verlag, 1980 | MR | Zbl

[21] Matveev S. V., Fomenko A. T., Sharko V. V., Kruglye funktsii Morsa i izoenergeticheskie poverkhnosti integriruemykh gamiltonovykh sistem, Preprint 86.76, In-t matematiki AN USSR, Kiev, 1986, 1–32 | MR

[22] Trofimov V. V., Fomenko A. T., “Geometriya skobok Puassona i metody integrirovaniya po Liuvillyu sistem na simmetricheskikh prostranstvakh”, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Noveishie dostizheniya, 29, 1986, 3–108 | MR

[23] Kozlov V. V., “O nekotorykh svoistvakh chastnykh integralov kanonicheskikh uravnenii”, Vestn. MGU. Ser. matem., mekhan., 1973, no. 1, 81–84 | Zbl

[24] Omeshkov L. A., “Bottovskie integraly nekotorykh integriruemykh gamiltonovykh sistem”, Geometriya, differentsialnye uravneniya i mekhanika, MGU, M., 1986, 115–117

[25] Fomenko A. T., Tsishang X., “O topologii trekhmernykh mnogoobrazii, voznikayuschikh v gamiltonovoi mekhanike”, Dokl. AN SSSR, 294:2 (1987), 283–287 | MR | Zbl