Branching of solutions and the nonexistence of first integrals in Hamiltonian mechanics. II

S. L. Ziglin

Funkcionalʹnyj analiz i ego priloženiâ, Tome 17 (1983) no. 1, pp. 8-23.

Bibliographie

[1] Springer Dzh., Vvedenie v teoriyu rimanovykh poverkhnostei, IL, M., 1960

[2] Arnold V.I., Dopolnitelnye glavy teorii obyknovennykh differentsialnykh uravnenii, Nauka, M., 1978 | MR

[3] Arnold V.I., Obyknovennye differentsialnye uravneniya, Nauka, M., 1971 | MR

[4] Arnold V.I., Krylov A.L., “Ravnomernoe raspredelenie tochek na sfere i nekotorye ergodicheskie svoistva reshenii obyknovennykh differentsialnykh uravnenii v kompleksnoi oblasti”, DAN SSSR, 148:1 (1963), 9–12 | MR

[5] Puankare A., Novye metody nebesnoi mekhaniki. Izbrannye trudy, Nauka, M., 1971

[6] Leng S., Algebra, Mir, M., 1968

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

[8] Van der Varden B.L., Algebra, Nauka, M., 1976 | MR

[9] Atya M., “$K$-teoriya i veschestvennost”, Atya M. Lektsii po $K$-teorii, Mir, M., 1967 | MR

[10] Kozlov V.V., “Nesuschestvovanie odnoznachnykh integralov i vetvlenie reshenii v dinamike tverdogo tela”, PMM, 42:3 (1978), 400–406 | MR | Zbl

[11] Kozlov V.V., Metody kachestvennogo analiza v dinamike tverdogo tela, Izd-vo MGU, M., 1980 | MR | Zbl

[12] Husson E., “Recherche des integrales algebraiques dans les mouvement d'un solide pesant autor d'un point fixe”, Ann. de la faculte des sciences de I'univ. de Toulouse, 2 ser., 8 (1906), 73–152 | MR | Zbl

[13] Arkhangelskii Yu.A., Analiticheskaya dinamika tverdogo tela, Nauka, M., 1977 | MR

[14] Ziglin S.L., “Vetvlenie reshenii, peresechenie separatris i nesuschestvovanie integrala v dinamike tverdogo tela”, Trudy MMO, 41, 1980, 287–303 | MR

[15] Kozlov V.V., “Nesuschestvovanie dopolnitelnogo integrala v zadache o dvizhenii nesimmetrichnogo tyazhelogo tverdogo tela okolo nepodvizhnoi tochki”, Vestn. MGU, ser. matem.-mekh., 1976, no. 6, 99–104 | MR | Zbl

[16] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, t. 3, Nauka, M., 1967 | MR

[17] Golubev V.V., Lektsii po analiticheskoi teorii differentsialnykh uravnenii, Gostekhizdat, M.–L., 1950 | MR

[18] Golubev V.V., Lektsii po integrirovaniyu uravnenii dvizheniya tyazhelogo tverdogo tela okolo nepodvizhnoi tochki, Gostekhizdat, M., 1953 | MR | Zbl

[19] Kozlov V.V., “O kachestvennom analize dvizheniya tyazhelogo tverdogo tela v sluchae Goryacheva–Chaplygina”, PMM, 41:2 (1977), 225–233 | MR | Zbl

[20] Forster O., Rimanovy poverkhnosti, Mir, M., 1980 | MR

[21] Henon M., Heiles C., “The applicability of the third integral of motion; some numerical experiments”, Astron. J., 69 (1964), 73–79 | DOI | MR

[22] Berry M.L., “Regular and irregular motions”, Topics in nonlinear dynamics, ed. Jorna S., American institute of physics, N. Y., 1978, 16–120 | MR

[23] Bogolyubov H.H., Shirkov D.V., Kvantovye polya, Nauka, M., 1980 | MR | Zbl

[24] Zakharov V.E., Ivanov M.F., Shur L.I., “Ob anomalno medlennoi stokhastizatsii v nekotorykh dvumernykh modelyakh teorii polya”, Pisma v ZhETF, 30:1 (1979), 39–44

[25] Demidovich B.P., Lektsii po matematicheskoi teorii ustoichivosti, Nauka, M., 1967 | MR

[26] Kovalevskaya S.V., Nauchnye trudy, Izd-vo AN SSSR, M., 1948 | MR

[27] Lyapunov A.M., “Ob odnom svoistve differentsialnykh uravnenii dvizheniya tyazhelogo tverdogo tela, imeyuschego nepodvizhnuyu tochku”, Soobsch. Kharkovsk. matem. ob-va, 2 ser., 4 (1894), 123–140

[28] Ziglin S.L., “Samoperesechenie kompleksnykh separatris i nesuschestvovanie integralov v gamiltonovykh sistemakh s polutora stepenyami svobody”, PMM, 45 (1981), 564–566 | MR | Zbl

[29] Ziglin S.L., “Vetvlenie reshenii i nesuschestvovanie pervykh integralov v gamiltonovoi mekhanike. I”, Funkts. analiz, 16:3 (1982), 30–41 | MR | Zbl