Geodesic
Singularities of integrable Hamiltonian systems with the same boundary foliation. An infinite series
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2016), pp. 14-20 
M. A. Tuzhilin. Singularities of integrable Hamiltonian systems with the same boundary foliation. An infinite series. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2016), pp. 14-20. http://geodesic.mathdoc.fr/item/VMUMM_2016_5_a1/
@article{VMUMM_2016_5_a1,
     author = {M. A. Tuzhilin},
     title = {Singularities of integrable {Hamiltonian} systems with the same boundary foliation. {An} infinite series},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {14--20},
     year = {2016},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2016_5_a1/}
}
TY  - JOUR
AU  - M. A. Tuzhilin
TI  - Singularities of integrable Hamiltonian systems with the same boundary foliation. An infinite series
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2016
SP  - 14
EP  - 20
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2016_5_a1/
LA  - ru
ID  - VMUMM_2016_5_a1
ER  - 
%0 Journal Article
%A M. A. Tuzhilin
%T Singularities of integrable Hamiltonian systems with the same boundary foliation. An infinite series
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2016
%P 14-20
%N 5
%U http://geodesic.mathdoc.fr/item/VMUMM_2016_5_a1/
%G ru
%F VMUMM_2016_5_a1

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

Four-dimensional momentum map singularities of integrable Hamiltonian systems of two degrees of freedom are considered. A construction of an infinite series of pairs of 4-dimensional saddle-saddle singularities is provided so that 4-singularities are not Liouville equivalent in each pair and the 2-foliations on their 3-boundaries are Liouville equivalent.

[1] 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

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

[3] Fomenko A.T., “Simplekticheskaya topologiya vpolne integriruemykh gamiltonovykh sistem”, Uspekhi matem. nauk, 44:1 (1989), 145–173 | MR

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

[5] Brailov A.V., Fomenko A.T., “Topologiya integralnykh mnogoobrazii vpolne integriruemykh gamiltonovykh sistem”, Matem. sb., 133:3 (1987), 375–385

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

[7] Fomenko A.T., Konyaev A.Yu., “Algebra and geometry through Hamiltonian systems”, Continuous and Distributed Systems. Theory and Applications, Solid Mechanics and Its Applications, 211, eds. V. Z. Zgurovsky, V. A. Sadovnichiy, Springer, 2014, 3–21 | DOI | MR | Zbl

[8] Fomenko A.T., Konyaev A.Yu., “New approach to symmetries and singularities in integrable Hamiltonian systems”, Topol. and its Appl., 159 (2012), 1964–1975 | DOI | MR | Zbl

[9] Bolsinov A.A., Fomenko A.T., Integriruemye gamiltonovy sistemy, v. 1, 2, Izd. dom “Udmurtskii universitet”, Izhevsk, 1999 | MR

[10] Williamson J., “On the algebraic problem concerning the normal forms of linear dynamical systems”, Amer. J. Math., 58:1 (1936), 141–163 | DOI | MR

[11] Williamson J., “On the normal forms of linear canonical transformations in dynamics”, Amer. J. Math., 59:1 (1937), 599–617 | DOI | MR

[12] Tuzhilin M.A., “Invarianty chetyrekhmernykh i trekhmernykh osobennostei integriruemykh sistem”, Dokl. RAN, 467:4 (2016), 385–388 | DOI | Zbl

[13] Nguen Tien Zung., “Symplectic topology of integrable Hamiltonian systems, I: Arnold–Liouville with singularities”, Compositio Mathematica, 101 (1996), 179–215 | MR

[14] Oshemkov A.A., “Funktsii Morsa na dvumernykh poverkhnostyakh. Kodirovanie osobennostei”, Tr. Matem. in-ta RAN, 205, 1994, 131–140 | Zbl

[15] Kudryavtseva E.A., Nikonov I.M., Fomenko A.T., “Maksimalno simmetrichnye kletochnye razbieniya poverkhnostei i ikh nakrytiya”, Matem. sb., 199:9 (2008), 3–96 | DOI | MR | Zbl