@article{SM_1994_77_2_a15,
author = {L. M. Lerman and Ya. L. Umanskii},
title = {Classification of four-dimensional integrable {Hamiltonian} systems and {Poisson} actions of~$\mathbb{R}^2$ in extended neighborhoods of simple singular {points.~I}},
journal = {Sbornik. Mathematics},
pages = {511--542},
year = {1994},
volume = {77},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1994_77_2_a15/}
}
TY - JOUR
AU - L. M. Lerman
AU - Ya. L. Umanskii
TI - Classification of four-dimensional integrable Hamiltonian systems and Poisson actions of $\mathbb{R}^2$ in extended neighborhoods of simple singular points. I
JO - Sbornik. Mathematics
PY - 1994
SP - 511
EP - 542
VL - 77
IS - 2
UR - http://geodesic.mathdoc.fr/item/SM_1994_77_2_a15/
LA - en
ID - SM_1994_77_2_a15
ER -
%0 Journal Article
%A L. M. Lerman
%A Ya. L. Umanskii
%T Classification of four-dimensional integrable Hamiltonian systems and Poisson actions of $\mathbb{R}^2$ in extended neighborhoods of simple singular points. I
%J Sbornik. Mathematics
%D 1994
%P 511-542
%V 77
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1994_77_2_a15/
%G en
%F SM_1994_77_2_a15
L. M. Lerman; Ya. L. Umanskii. Classification of four-dimensional integrable Hamiltonian systems and Poisson actions of $\mathbb{R}^2$ in extended neighborhoods of simple singular points. I. Sbornik. Mathematics, Tome 77 (1994) no. 2, pp. 511-542. http://geodesic.mathdoc.fr/item/SM_1994_77_2_a15/
[1] Smeil S., “Topologiya i mekhanika”, UMN, 27:2 (1972), 77–123 | MR | Zbl
[2] Selecta Math. Sovietica, 6:4 (1987), 365–396 | MR | Zbl
[3] Selecta Math. Sovietica, 7:1 (1988), 39–48 | MR | MR | Zbl | Zbl
[4] Selecta Math. Sovietica, 9:1 (1990), 59–67 | MR | Zbl
[5] Lerman L.M., Umanskii Ya.L., “O klassifikatsii chetyrekhmernykh integriruemykh gamiltonovykh sistem v rasshirennykh okrestnostyakh prostykh osobykh tochek”, Metody kachestv. teorii i teorii bifurkatsii, Mezhvuz. temat. sb. nauch. tr., ed. E.A. Leontovich-Andronova, Gork. gos.un-t, Gorkii, 1988, 67–75
[6] Fomenko A.T., “Topologiya poverkhnostei postoyannoi energii integriruemykh gamiltonovykh sistem i prepyatstviya k integriruemosti”, Izv. AN SSSR. Ser. matem., 50:6 (1986), 1276–1307 | MR | Zbl
[7] Fomenko A.T., “Topologicheskie invarianty gamiltonovykh sistem, integriruemykh po Liuvillyu”, Funktsion. analiz i ego prilozheniya, 22:4 (1988), 38–51 | MR | Zbl
[8] Fomenko A.T., Tsishang Kh., “Kriterii topologicheskoi ekvivalentnosti integriruemykh gamiltonovykh sistem s dvumya stepenyami svobody”, Izv. AN SSSR. Ser. matem., 54:3 (1990), 546–575 | MR | Zbl
[9] Arnold V.I., Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1974 | MR
[10] Marsden J.R., Weinstein A., “Reduction of symplectic manifolds with symmetry”, Rept. Math. Phys., 5:1 (1974), 121–130 | DOI | MR | Zbl
[11] Arnold V.I., Varchenko A.N., Gusein-Zade S.M., Osobennosti differentsiruemykh otobrazhenii, Nauka, M., 1982 | MR
[12] Russmann H., “Uber das verhalten analytischer Hamiltonscher differentialgleichungen in der nahe einer gleichgewichtslosung”, Math. Ann., 154 (1964), 285–300 | DOI | MR
[13] Elliasson L.H., “Normal forms for Hamiltonian systems with Poisson commuting integrals. Elliptic case”, Comment. Math. Helv., 65 (1990), 4–35 | DOI | MR
[14] Bishop R., Krittenden R., Geometriya mnogoobrazii, Mir, M., 1967 | MR | Zbl
[15] Bautin N.N., Leontovich E.A., Metody i priemy kachestvennogo issledovaniya dinamicheskikh sistem, Nauka, M., 1976 | MR
[16] Shoshitaishvili A.N., “Bifurkatsii topologicheskogo tipa vektornogo polya vblizi osoboi tochki”, Tr. semin. im. I.G. Petrovskogo, 1, 1975, 279–309
[17] Fomenko A.T., “Teoriya bordizmov integriruemykh gamiltonovykh nevyrozhdennykh sistem s dvumya stepenyami svobody. Novyi topologicheskii invariant mnogomernykh integriruemykh sistem”, Izvestiya AN SSSR. Ser. matem., 55:4 (1991), 747–779 | MR
[18] Bolsinov A.V., “Methods of calculation of the Fomenko–Zieschang invariant”, Adv. in Soviet Math., 6 (1991), 147–183 | MR | Zbl