Geodesic
Isoenergy manifolds of integrable billiard books
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2020), pp. 12-22 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider a class of integrable Hamiltonian systems with two degrees of freedom — billiard books, which are generalizations of billiards bounded by arcs of confocal quadrics. The first issue arising in the study of billiards is concerned with the topology of the phase space and the isoenergy manifold. We prove that the phase space and the isoenergy manifold of any billiard book are actually piecewise manifolds. 
@article{VMUMM_2020_4_a1,
     author = {I. S. Kharcheva},
     title = {Isoenergy manifolds of integrable billiard books},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {12--22},
     year = {2020},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2020_4_a1/}
}
TY  - JOUR
AU  - I. S. Kharcheva
TI  - Isoenergy manifolds of integrable billiard books
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2020
SP  - 12
EP  - 22
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2020_4_a1/
LA  - ru
ID  - VMUMM_2020_4_a1
ER  - 
%0 Journal Article
%A I. S. Kharcheva
%T Isoenergy manifolds of integrable billiard books
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2020
%P 12-22
%N 4
%U http://geodesic.mathdoc.fr/item/VMUMM_2020_4_a1/
%G ru
%F VMUMM_2020_4_a1
I. S. Kharcheva. Isoenergy manifolds of integrable billiard books. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2020), pp. 12-22. http://geodesic.mathdoc.fr/item/VMUMM_2020_4_a1/

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

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

[3] Dragovic V., Radnovic M., “Bifurcations of Liouville tori in elliptical billiards”, Regul. and Chaotic Dyn., 14:4–5 (2009), 479–494 | DOI | MR | Zbl

[4] Dragovich V., Radnovich M., Integriruemye billiardy, kvadriki i mnogomernye porizmy Ponsele, NITs RKhD, M.–Izhevsk, 2010

[5] Fokicheva V. V., “Opisanie osobennostei sistemy “bilyard v ellipse””, Vestn. Mosk. un-ta. Matem. Mekhan., 2012, no. 5, 31–34 | MR | Zbl

[6] Fokicheva V. V., “Klassifikatsiya billiardnykh dvizhenii v oblastyakh, ogranichennykh sofokusnymi parabolami”, Matem. sb., 205:8 (2014), 139–160 | MR | Zbl

[7] Fokicheva V. V., “Opisanie osobennostei sistemy bilyarda v oblastyakh, ogranichennykh sofokusnymi ellipsami i giperbolami”, Vestn. Mosk. un-ta. Matem. Mekhan., 2014, no. 4, 18–27 | MR | Zbl

[8] Fokicheva V. V., Fomenko A. T., “Integriruemye billiardy modeliruyut vazhnye integriruemye sluchai dinamiki tverdogo tela”, Dokl. RAN. Matematika, 465:2 (2015), 1–4

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

[10] Vedyushkina V. V., Fomenko A. T., Kharcheva 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

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

[12] Vedyushkina V. V. (Fokicheva), Fomenko A. T., “Integriruemye topologicheskie billiardy i ekvivalentnye dinamicheskie sistemy”, Izv. RAN. Ser. matem., 81:4 (2017), 3–50 | MR