The Arnold-Moser theorem and the stability problem in new models of celestial dynamics
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 43 (2003) no. 2, pp. 203-211 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

@article{ZVMMF_2003_43_2_a4,
     author = {E. A. Grebenikov and D. Kozak-Skovorodkina and M. Yakubyak},
     title = {The {Arnold-Moser} theorem and the stability problem in new models of celestial dynamics},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {203--211},
     year = {2003},
     volume = {43},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_2_a4/}
}
TY  - JOUR
AU  - E. A. Grebenikov
AU  - D. Kozak-Skovorodkina
AU  - M. Yakubyak
TI  - The Arnold-Moser theorem and the stability problem in new models of celestial dynamics
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2003
SP  - 203
EP  - 211
VL  - 43
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_2_a4/
LA  - ru
ID  - ZVMMF_2003_43_2_a4
ER  - 
%0 Journal Article
%A E. A. Grebenikov
%A D. Kozak-Skovorodkina
%A M. Yakubyak
%T The Arnold-Moser theorem and the stability problem in new models of celestial dynamics
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2003
%P 203-211
%V 43
%N 2
%U http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_2_a4/
%G ru
%F ZVMMF_2003_43_2_a4
E. A. Grebenikov; D. Kozak-Skovorodkina; M. Yakubyak. The Arnold-Moser theorem and the stability problem in new models of celestial dynamics. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 43 (2003) no. 2, pp. 203-211. http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_2_a4/

[1] Grebenicov E., “Two new dynamical models in celestial mechanics”, Rom. Astron. J., 8:1 (1998), 13–19

[2] Wintner A., The analytical foundations of celestial mechanics, Univ. Press, Princeton, 1941 | MR

[3] Elmabsout B., “Sur l'existence de certaines configurations d'équillibre rélatif dans le probléme des $n$ corps”, Celestial Mech. and Dynamical Astron., 4:1 (1988), 131–151 | MR | Zbl

[4] Grebenikov E. A., “Suschestvovanie tochnykh simmetrichnykh reshenii v ploskoi nyutonovoi probleme mnogikh tel”, Matem. modelirovanie, 10:8 (1998), 74–80 | MR | Zbl

[5] Arnold V. I., Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1974 | MR

[6] Markeev A. P., Tochki libratsii v nebesnoi mekhanike i kosmodinamike, Nauka, M., 1978 | Zbl

[7] Mozer Yu., Lektsii o gamiltonovykh sistemakh, Mir, M., 1973

[8] Birkgof Dzh. D., Dinamicheskie sistemy, Gostekhteorizdat, M.–L., 1941

[9] Lyapunov A. M., Sobr. soch., v. 1, Obschaya zadacha ob ustoichivosti dvizheniya, Izd-vo AN SSSR, M.–L., 1954 | MR

[10] Grebenicov E. A., Gadomski L. Ya., “The existence conditions for equilibrium in a bounded circular many-body problem”, Proc. Steklov Inst. Math., 223, M., 1998, 159–162

[11] Wolfram S., The mathematica-book, Univ. Press, Cambridge, 1996 | MR

[12] Kozak D., Oniszk E., “Equilibrium points in the restricted four-body problem: sufficcient conditiones for linear stability”, Rom. Astron. J., 8:1 (1998), 27–31 | MR

[13] Kozak D., Onishk E., “Primenenie kompyuternoi sistemy MATEMATIKA dlya opredeleniya koordinat polozhenii ravnovesiya v gravitatsionnoi modeli chetyrekh tel Grebenikova–Elmabsuta”, Neliniini kolivannya, 2, no. 1, Kiev, 1999, 16–19 | MR

[14] Yakubyak M., “Dostatochnye usloviya lineinoi ustoichivosti polozhenii ravnovesiya v gravitatsionnoi nyutonovoi modeli shesti tel”, Neliniini kolivannya, 2, no. 1, Kiev, 1999, 138–144 | MR | Zbl

[15] Grebenicov E., Kozak-Skoworodkin D., Jakubiak M., “The algebraic problems of the normalization in Hamiltonian theory”, “MATHEMATICA” System in Teaching and Res., Proc. Sec. Internat. Workshop (Siedlce, 2000, January 28–30)

[16] Arnold V. I., “Ob ustoichivosti polozhenii ravnovesiya gamiltonovoi sistemy obyknovennykh differentsialnykh uravnenii v obschem ellipticheskom sluchae”, Dokl. AN SSSR, 137:2 (1961), 255–257 | MR

[17] Grebenikov E. A., Mitropolskii Yu. A., Ryabov Yu. A., Vvedenie v rezonansnuyu analiticheskuyu dinamiku, Izd-vo “Yanus-K”, M., 1999 | MR

[18] Kozak D., Yakubyak M., “Problema suschestvovaniya rezonansov chastot v ogranichennoi nyutonovoi probleme shesti i semi tel”, Nelineinyi analiz i gomografich. dinamika, 1, VTs RAN, M., 1999, 20–40