Voir la notice de l'article provenant de la source Math-Net.Ru
@article{FPM_2016_21_6_a10, author = {D. A. Fedoseev and A. T. Fomenko}, title = {Noncompact bifurcations of integrable dynamic systems}, journal = {Fundamentalʹna\^a i prikladna\^a matematika}, pages = {217--243}, publisher = {mathdoc}, volume = {21}, number = {6}, year = {2016}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/FPM_2016_21_6_a10/} }
TY - JOUR AU - D. A. Fedoseev AU - A. T. Fomenko TI - Noncompact bifurcations of integrable dynamic systems JO - Fundamentalʹnaâ i prikladnaâ matematika PY - 2016 SP - 217 EP - 243 VL - 21 IS - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FPM_2016_21_6_a10/ LA - ru ID - FPM_2016_21_6_a10 ER -
D. A. Fedoseev; A. T. Fomenko. Noncompact bifurcations of integrable dynamic systems. Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 6, pp. 217-243. http://geodesic.mathdoc.fr/item/FPM_2016_21_6_a10/
[1] Aleshkin K. R., “Topologiya integriruemykh sistem s nepolnymi polyami”, Matem. sb., 205:9 (2014), 49–64 | DOI | MR | Zbl
[2] Borisov A. V., Mamaev I. S., Sokolov V. V., “Novyi integriruemyi sluchai na $\mathrm{so}(4)$”, Dokl. RAN, 381:5 (2011), 614–615
[3] Zagryadskii O. A., Bertranovskie sistemy i ikh fazovoe prostranstvo, Nauka i obrazovanie, 12, 2014
[4] Zagryadskii O. A., Kudryavtseva E. A., Fedoseev D. A., “Obobschenie teoremy Bertrana na poverkhnosti vrascheniya”, Matem. sb., 203:8 (2012), 39–78 | DOI | MR | Zbl
[5] Kudryavtseva E. A., Lepskii T. A., “Topologiya sloenii i teorema Liuvillya dlya integriruemykh sistem s nepolnymi potokami”, Tr. sem. po vektornomu i tenzornomu analizu, 27, 2011, 106–149
[6] 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
[7] Kudryavtseva E. A., Fedoseev D. A., “Mekhanicheskie sistemy s zamknutymi traektoriyami na mnogoobraziyakh vrascheniya”, Matem. sb., 206:5 (2015), 107–126 | DOI | MR | Zbl
[8] Kudryavtseva E. A., Fomenko A. T., “Gruppy simmetrii pravilnykh funktsii Morsa na poverkhnostyakh”, Dokl. RAN, seriya matematika, 446:6 (2012), 615–617 | Zbl
[9] Nguen T. Z., Fomenko A. T., “Topologicheskaya klassifikatsiya integriruemykh nevyrozhdennykh gamiltonianov na izoenergeticheskoi trekhmernoi sfere”, UMN, 45:6 (1990), 91–111 | MR
[10] Novikov D. V., “Topologicheskie osobennosti integriruemogo sluchaya Sokolova na algebre Li $e(3)$”, Matem. sb., 202:5 (2011), 127–160 | DOI | MR
[11] Sokolov V. V., “Novyi integriruemyi sluchai dlya uravnenii Kirkhgofa”, TMF, 129:1 (2001), 31–37 | DOI | MR | Zbl
[12] Sokolov V. V., “Ob odnom klasse kvadratichnykh gamiltonianov na $\mathrm{so}(4)$”, Dokl. RAN, 394:5 (2004), 602–605 | MR | Zbl
[13] Fedoseev D. A., “Bifurkatsionnye diagrammy naturalnykh gamiltonovykh sistem na mnogoobraziyakh Bertrana”, Vestn. Mosk. un-ta. Ser. 1. Matematika, mekhanika, 2015, no. 1, 62–65 | Zbl
[14] Fomenko A. T., “Teoriya Morsa integriruemykh gamiltonovykh sistem”, DAN SSSR, 287:5 (1986), 1071–1075 | MR | Zbl
[15] Fomenko A. T., “Topologiya poverkhnostei postoyannoi energii nekotorykh integriruemykh gamiltonovykh sistem i prepyatstviya k integriruemosti”, Izv. AN SSSR. Ser. matem., 50:6 (1986), 1276–1307 | MR | Zbl
[16] Fomenko A. T., “Topologicheskie invarianty gamiltonovykh sistem, integriruemykh po Liuvillyu”, Funkts. analiz i ego pril., 22:4 (1988), 38–51 | MR | Zbl
[17] Fomenko A. T., “Simplekticheskaya topologiya vpolne integriruemykh gamiltonovykh sistem”, UMN, 44:1 (1989), 145–173 | MR
[18] Fomenko A. T., “Topologicheskii invariant, grubo klassifitsiruyuschii integriruemye strogo nevyrozhdennye gamiltoniany na chetyrekhmernykh simplekticheskikh mnogoobraziyakh”, Funkts. anal. i ego pril., 25:4 (1991), 23–35 | MR
[19] Fomenko A. T., Bolsinov A. V., Integriruemye gamiltonovy sistemy, Izd. dom «Udmurtskii universitet», 1999
[20] Fomenko A. T., Tsishang Kh., “O topologii trekhmernykh mnogoobrazii, voznikayuschikh v gamiltonovoi mekhanike”, DAN SSSR, 294:2 (1986), 283–287
[21] Besse A., Manifolds all of whose geodesics are closed, Springer, Berlin, 1978 | MR | Zbl
[22] Fomenko A. T., Konyaev A. Yu., “New approach to symmetries and singularities in integrable Hamiltonian systems”, Topol. Its Appl., 159 (2012), 1964–1975 | DOI | MR | Zbl
[23] Fomenko A. T., Konyaev A. Yu., “Algebra and Geometry Through Hamiltonian Systems”, Continuous and Distributed Systems. Theory and Applications, Solid Mechanics and Its Applications, 211, eds. V. Z. Zgurovsky, V. A. Sadovnichiy, Springer, Berlin, 2014, 3–21 | DOI | MR | Zbl
[24] Gavrilov L., “Bifurcations of invariant manifolds in the generalized Henon–Heiles system”, Physica D, 34 (1989), 223–239 | DOI | MR | Zbl