Geodesic
Local modeling of Liouville foliations by billiards: implementation of edge invariants
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2021), pp. 28-32 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The local case of A. Fomenko conjecture on the possibility of modeling Liouville foliations by integrable billiards is discussed. An extended version of its statements on numerical invariants on the edge of the Fomenko–Zieschang invariant of the Liouville foliation is proved. We show the realization of the Liouville foliation with some combinations of numerical marks values on a fixed edge by an appropriate class of integrable billiards. 
@article{VMUMM_2021_2_a4,
     author = {V. V. Vedyushkina},
     title = {Local modeling of {Liouville} foliations by billiards: implementation of edge invariants},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {28--32},
     year = {2021},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2021_2_a4/}
}
TY  - JOUR
AU  - V. V. Vedyushkina
TI  - Local modeling of Liouville foliations by billiards: implementation of edge invariants
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2021
SP  - 28
EP  - 32
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2021_2_a4/
LA  - ru
ID  - VMUMM_2021_2_a4
ER  - 
%0 Journal Article
%A V. V. Vedyushkina
%T Local modeling of Liouville foliations by billiards: implementation of edge invariants
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2021
%P 28-32
%N 2
%U http://geodesic.mathdoc.fr/item/VMUMM_2021_2_a4/
%G ru
%F VMUMM_2021_2_a4
V. V. Vedyushkina. Local modeling of Liouville foliations by billiards: implementation of edge invariants. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2021), pp. 28-32. http://geodesic.mathdoc.fr/item/VMUMM_2021_2_a4/

[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., Fomenko A.T., “Integriruemye topologicheskie billiardy i ekvivalentnye dinamicheskie sistemy”, Izv. RAN. Ser. matem., 81:4 (2017), 20–67 | MR | Zbl

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

[5] Vedyushkina V.V., Fomenko A.T., “Integriruemye geodezicheskie potoki na orientiruemykh dvumernykh poverkhnostyakh i topologicheskie billiardy”, Izv. RAN. Ser. matem., 83:5 (2019), 3–43 | MR

[6] Kozlov V.V., Treschev D.V., Geneticheskoe vvedenie v dinamiku sistem s udarami, Izd-vo MGU, M., 1991

[7] Bolsinov A.V., Fomenko A.T., Integriruemye gamiltonovy sistemy. Geometriya, topologiya, klassifikatsiya, v. 1, 2, NITs “Regulyarnaya i khaoticheskaya dinamika”, Izhevsk, 1999

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

[9] Fomenko A.T., “Simplekticheskaya topologiya vpolne integriruemykh gamiltonovykh sistem”, Uspekhi matem. nauk, 44 (265):5 (1989), 145–173 | MR

[10] Vedyushkina V.V., Kibkalo V.A., Fomenko A.T., “Topologicheskoe modelirovanie integriruemykh sistem billiardami: realizatsiya chislovykh invariantov”, Dokl. RAN, 493:1 (2020), 9–12 | MR

[11] Vedyushkina V.V., Kibkalo V.A., “Realizatsiya bilyardami chislovogo invarianta rassloeniya Zeiferta integriruemykh sistem”, Vestn. Mosk. un-ta. Matem. Mekhan., 2020, no. 4, 22–28 | MR | Zbl

[12] Vedyushkina V.V., “Integriruemye billiardy realizuyut toricheskie sloeniya na linzovykh prostranstvakh i 3-tore”, Matem. sb., 211:1 (2020), 46–73 | MR | Zbl

[13] Fomenko A.T., Vedyushkina V.V., “Implementation of integrable systems by topological, geodesic billiards with potential and magnetic field”, Russ. J. Math. Phys., 26:3 (2019), 320–333 | DOI | MR | Zbl

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

[15] Vedyushkina V.V., Fomenko A.T., Kharchëva I.S., “Modelirovanie nevyrozhdennykh bifurkatsii zamykanii reshenii integriruemykh sistem s dvumya stepenyami svobody integriruemymi topologicheskimi billiardami”, Dokl. RAN, 479:6 (2018), 607–610 | MR | Zbl