Realization of numeriсal invariant of the Siefert bundle of integrable systems by billiards
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2020), pp. 22-28 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A local case of A. Fomenko conjecture on possibility of realization of a Liouville foliation with arbitrary topological Fomenko–Zieschang invariant (which is a graph with numerical marks) is discussed. In the class of billiard books, a foliation with arbitrary value of one integer mark (that corresponds to Euler class of one Seifert submanifold) was realized.
@article{VMUMM_2020_4_a2,
     author = {V. V. Vedyushkina and V. A. Kibkalo},
     title = {Realization of numeri{\cyrs}al invariant of the {Siefert} bundle of integrable systems by billiards},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {22--28},
     year = {2020},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2020_4_a2/}
}
TY  - JOUR
AU  - V. V. Vedyushkina
AU  - V. A. Kibkalo
TI  - Realization of numeriсal invariant of the Siefert bundle of integrable systems by billiards
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2020
SP  - 22
EP  - 28
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2020_4_a2/
LA  - ru
ID  - VMUMM_2020_4_a2
ER  - 
%0 Journal Article
%A V. V. Vedyushkina
%A V. A. Kibkalo
%T Realization of numeriсal invariant of the Siefert bundle of integrable systems by billiards
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2020
%P 22-28
%N 4
%U http://geodesic.mathdoc.fr/item/VMUMM_2020_4_a2/
%G ru
%F VMUMM_2020_4_a2
V. V. Vedyushkina; V. A. Kibkalo. Realization of numeriсal invariant of the Siefert bundle of integrable systems by billiards. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2020), pp. 22-28. http://geodesic.mathdoc.fr/item/VMUMM_2020_4_a2/

[1] Vedyushkina V. V., Fomenko A. T., “Bilyardy i integriruemost v geometrii i fizike. Novyi vzglyad i novye vozmozhnosti”, Vestn. Mosk. un-ta. Matem. Mekhan., 2019, no. 3, 15–25 | MR | Zbl

[2] Fomenko A. T., Tsishang Kh., “Topologicheskii invariant i kriterii ekvivalentnosti integriruemykh gamiltonovykh sistem s dvumya stepenyami svobody”, Izv. AN SSSR. Ser. matem., 54:3 (1990), 546–575 | Zbl

[3] Vedyushkina V. V., Kharcheva I. S., “Billiardnye knizhki modeliruyut vse trekhmernye bifurkatsii integriruemykh gamiltonovykh sistem”, Matem. sb., 209:12 (2018), 17–56 | MR | Zbl

[4] Bolsinov A. V., Fomenko A. T., Integriruemye gamiltonovy sistemy. Geometriya, topologiya, klassifikatsiya, v. 1, 2, NITs “RKhD”, Izhevsk, 1999

[5] Kozlov V. V., Treschev V. V., Billiardy. Geneticheskoe vvedenie v dinamiku sistem s udarami, Izd-vo MGU, M., 1991 | MR

[6] Fokicheva V. V., “Topologicheskaya klassifikatsiya billiardov v lokalno ploskikh oblastyakh, ogranichennykh dugami sofokusnykh kvadrik”, Matem. sb., 206:10 (2015), 127–176 | MR | Zbl

[7] Fokicheva V. V., Fomenko A. T., “Integriruemye billiardy modeliruyut vazhnye integriruemye sluchai dinamiki tverdogo tela”, Dokl. RAN, 465:2 (2015), 150–153 | MR | Zbl

[8] Vedyushkina V. V., “Invarianty Fomenko–Tsishanga nevypuklykh topologicheskikh billiardov”, Matem. sb., 210:3 (2019), 17–74 | MR | Zbl