Geodesic
Partially symmetric height atoms
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2018), pp. 33-41 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We present a partial classification of vertical atoms whose symmetry groups act transitively on the rings of the atoms. A total of 9 infinite series and 19 special cases are described. 
@article{VMUMM_2018_2_a3,
     author = {V. A. Trifonova},
     title = {Partially symmetric height atoms},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {33--41},
     year = {2018},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2018_2_a3/}
}
TY  - JOUR
AU  - V. A. Trifonova
TI  - Partially symmetric height atoms
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2018
SP  - 33
EP  - 41
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2018_2_a3/
LA  - ru
ID  - VMUMM_2018_2_a3
ER  - 
%0 Journal Article
%A V. A. Trifonova
%T Partially symmetric height atoms
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2018
%P 33-41
%N 2
%U http://geodesic.mathdoc.fr/item/VMUMM_2018_2_a3/
%G ru
%F VMUMM_2018_2_a3
V. A. Trifonova. Partially symmetric height atoms. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2018), pp. 33-41. http://geodesic.mathdoc.fr/item/VMUMM_2018_2_a3/

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

[2] Manturov V.O., “Bifurkatsii, atomy i uzly”, Vestn. Mosk. un-ta. Matem. Mekhan., 2000, no. 1, 3–8 | Zbl

[3] 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

[4] 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

[5] 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

[6] Kudryavtseva E.A., Nikonov I.M., Fomenko A.T., “Simmetrichnye i neprivodimye abstraktnye mnogogranniki”, Sovremennye problemy matematiki i mekhaniki, ed. A. T. Fomenko, Izd-vo MGU, M., 2009, 58–97 | MR

[7] Nikonov I.M., “Vysotnye atomy s tranzitivnoi na vershinakh gruppoi simmetrii”, Vestn. Mosk. un-ta. Matem. Mekhan., 2016, no. 6, 1–10

[8] Volchanetskii N.V., Nikonov I.M., “Maksimalno simmetrichnye vysotnye atomy”, Vestn. Mosk. un-ta. Matem. Mekhan., 2013, no. 2, 3–6 | MR | Zbl

[9] 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

[10] Kudryavtseva E.A., Fomenko A.T., “Gruppy simmetrii pravilnykh funktsii Morsa na poverkhnostyakh”, Dokl. RAN, 446:6 (2012), 615–617 | Zbl

[11] Kudryavtseva E.A., Fomenko A.T., “Lyubaya konechnaya gruppa yavlyaetsya gruppoi simmetrii nekotoroi karty (“atoma-bifurkatsii”)”, Vestn. Mosk. un-ta. Matem. Mekhan., 2013, no. 3, 21–29 | MR | Zbl

[12] Vedyushkina (Fokicheva) V.V., Fomenko A.T., “Integriruemye topologicheskie billiardy i ekvivalentnye dinamicheskie sistemy”, Izv. RAN. Ser. matem., 2017, no. 4, 20–67 | DOI | MR | Zbl

[13] Vedyushkina (Fokicheva) V.V., Fomenko A.T., “Billiard systems as the models for the rigid body dynamics”, Advances in Dynamical Systems and Control, Studies in Systems, Decision and Control, 69, eds. V. A. Sadovnichiy, M. Z. Zgurovsky, Springer Int. Publ., Switzerland, 2016, 13–32 | DOI | MR

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

[15] Fomenko A.T., Nikolaenko S.S., “The Chaplygin case in dynamics of a rigid body in fluid is orbitally equivalent to the Euler case in rigid body dynamics and to the Jacobi problem about geodesics on the ellipsoid”, J. Geom. and Phys., 87 (2015), 115–133 | DOI | MR | Zbl

[16] Fomenko A.T., Kantonistova E.O., “Topological classification of geodesic flows on revolution 2-surfaces with potential”, Continuous and Distributed Systems II. Theory and Applications, Ch. 2, eds. V. A. Sadovnichiy, M. Z. Zgurovsky, Springer Int. Publ., Switzerland, Cham–Heidelberg–N.Y.–Dordrecht–London, 2015, 11–27 | MR | Zbl