Geodesic
Bifurcations of periodic solutions near triangular libration points in the three-body problem
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2010), pp. 82-89 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider the problem on bifurcations of periodic solutions near triangular libration points in the plane elliptic bounded three-body problem. We determine values of the mass parameter such that at small values of the eccentricity the problem has non-stationary periodic solutions close to a libration point. We determine bifurcation types and study the asymptotic for the mentioned solutions.
Keywords: three-body problem, libration points, periodic solutions, asymptotic formulas.
Mots-clés : bifurcation 
@article{IVM_2010_6_a7,
     author = {M. G. Yumagulov and O. N. Belikova},
     title = {Bifurcations of periodic solutions near triangular libration points in the three-body problem},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {82--89},
     year = {2010},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_6_a7/}
}
TY  - JOUR
AU  - M. G. Yumagulov
AU  - O. N. Belikova
TI  - Bifurcations of periodic solutions near triangular libration points in the three-body problem
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2010
SP  - 82
EP  - 89
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/IVM_2010_6_a7/
LA  - ru
ID  - IVM_2010_6_a7
ER  - 
%0 Journal Article
%A M. G. Yumagulov
%A O. N. Belikova
%T Bifurcations of periodic solutions near triangular libration points in the three-body problem
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2010
%P 82-89
%N 6
%U http://geodesic.mathdoc.fr/item/IVM_2010_6_a7/
%G ru
%F IVM_2010_6_a7
M. G. Yumagulov; O. N. Belikova. Bifurcations of periodic solutions near triangular libration points in the three-body problem. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2010), pp. 82-89. http://geodesic.mathdoc.fr/item/IVM_2010_6_a7/

[1] Markeev A. P., Tochki libratsii v nebesnoi mekhanike i kosmodinamike, Nauka, M., 1978, 312 pp.

[2] Duboshin G. N., Nebesnaya mekhanika. Analiticheskie i kachestvennye metody, Nauka, M., 1978, 456 pp.

[3] Marshal K., Zadacha trekh tel, Institut kompyuternykh issledovanii, Moskva–Izhevsk, 2004, 640 pp.

[4] Simo K., Smeil S., Shensine A. i dr., Sovremennye problemy khaosa i nelineinosti, Institut kompyuternykh issledovanii, Moskva–Izhevsk, 2002, 304 pp.

[5] Simo K., “Periodicheskie traektorii ploskoi zadachi $N$ tel s ravnymi massami i telami, dvizhuschimisya po odnoi i toi zhe traektorii”, Otnositelnye ravnovesiya. Periodicheskie resheniya, Sb. rabot, Institut kompyuterykh issledovanii, Moskva–Izhevsk, 2006, 175–201

[6] Gukenkheimer Dzh., Kholms F., Nelineinye kolebaniya, dinamicheskie sistemy i bifurkatsii vektornykh polei, Institut kompyuternykh issledovanii, Moskva–Izhevsk, 2002, 560 pp.

[7] Ikromov A., “O $6\pi$-periodicheskikh resheniyakh ploskoi ogranichennoi ellipticheskoi zadachi trekh tel”, Astron. zhurn., 61:4 (1984), 800–805 | MR | Zbl

[8] Evteev V. P., “Periodicheskie resheniya ploskoi ellipticheskoi zadachi trekh tel”, Kosmicheskie issledovaniya, 26:5 (1988), 785–787 | MR

[9] Krasnoselskii M. A., Zabreiko P. P., Geometricheskie metody nelineinogo analiza, Nauka, M., 1975, 511 pp. | MR

[10] Ibragimova L. S., Yumagulov M. G., “Funktsionalizatsiya parametra i ee prilozheniya v zadache o lokalnykh bifurkatsiyakh dinamicheskikh sistem”, Avtomatika i telemekhanika, 2007, no. 4, 3–12 | MR | Zbl

[11] Vainberg M. M., Trenogin V. A., Teoriya vetvleniya reshenii nelineinykh uravnenii, Nauka, M., 1969, 527 pp. | MR | Zbl