Valerii Vladimirovich Trofimov

D. V. Georgievskii ; M. V. Shamolin

Contemporary Mathematics. Fundamental Directions, Geometry and mechanics, Tome 23 (2007), pp. 5-15.

Bibliographie

[1] “Vlozhenie konechnykh grupp regulyarnymi elementami v kompaktnye gruppy Li”, Dokl. AN SSSR, 226:4 (1976), 785–786 | MR | Zbl

[2] “Vlozhenie konechnykh grupp regulyarnymi elementami v kompaktnye gruppy Li”, Tr. semin. po vektor. i tenzor. anal., no. 19, 1979, 178–201 | Zbl

[3] “Uravneniya Eilera na borelevskikh podalgebrakh poluprostykh algebr Li”, Izv. AN SSSR. Ser. mat., 43:3 (1979), 714–732 | MR | Zbl

[4] “O polnoi integriruemosti uravnenii Eilera na borelevskikh podalgebrakh prostykh algebr Li”, 7 Vses. konf. po sovr. probl. geometrii, Tez. dokl., Minsk, 1979, 201

[5] Polnaya integriruemost uravnenii Eilera na borelevskikh podalgebrakh prostykh algebr Li, Diss. na soisk. uchenoi stepeni k.f.-m.n., MGU, M., 1980, 137 pp. | Zbl

[6] “Konechnomernye predstavleniya algebr Li i vpolne integriruemye sistemy”, Mat. sb., 111(153):4 (1980), 610–621 | MR | Zbl

[7] “Uravneniya Eilera na konechnomernykh razreshimykh gruppakh Li”, Izv. AN SSSR. Ser. mat., 44:5 (1980), 1191–1199 | MR | Zbl

[8] “Metodika postroeniya gamiltonovykh potokov na simmetricheskikh prostranstvakh i integriruemost nekotorykh gidrodinamicheskikh sistem”, Dokl. AN SSSR, 254:6 (1980), 1349–1353 (with A. T. Fomenko) | MR

[9] A. N. Kolmogorov (red.), “O polnoi integriruemosti uravnenii Eilera na nekompaktnykh algebrakh Li”, Nekotorye voprosy matematiki i mekhaniki, MGU, M., 1981, 20–21

[10] “O realizatsii mekhanicheskikh sistem na orbitakh razreshimykh algebr Li”, Izv. AN SSSR. Ser. Mekh. tv. tela, 3 (1981), 163 (with A. T. Fomenko)

[11] “O funktsii defekta rimanovykh mnogoobrazii”, Vestn. MGU. Ser. 1, 5 (1981), 54–57 | Zbl

[12] “Teoretiko-gruppovaya interpretatsiya uravnenii magnitnoi gidrodinamiki idealno provodyaschei zhidkosti”, Nelineinye kolebaniya i teoriya upravleniya, Udmurtskii gos. universitet, Izhevsk, 1981, 118–124

[13] “Vpolne integriruemye geodezicheskie potoki levoinvariantnykh metrik na gruppakh Li, svyazannye s kommutativnymi algebrami s dvoistvennostyu Puankare”, Dokl. AN SSSR, 263:4 (1982), 812–816 | MR | Zbl

[14] “Pervye integraly priblizhenii Galerkina uravnenii magnitnoi gidrodinamiki”, Nekotorye voprosy prikladnoi matematiki i programmnogo obespecheniya EVM, MGU, M., 1982, 7–8

[15] “Vpolne integriruemye sistemy gidrodinamicheskogo tipa i algebry s dvoistvennostyu Puankare”, Shkola po teorii operatorov v funktsionalnykh prostranstvakh, Minsk, 1982, 192–193

[16] “Gruppovye neinvariantnye simplekticheskie struktury i gamiltonovy potoki na simmetricheskikh prostranstvakh”, Tr. semin. po vektor. i tenzor. anal., no. 21, 1983, 23–83 (with A. T. Fomenko) | Zbl

[17] “Poluinvarianty koprisoedinennogo predstavleniya borelevskikh podalgebr prostykh algebr Li”, Tr. semin. po vektor. i tenzor. anal., no. 21, 1983, 84–105 | Zbl

[18] “O vpolne integriruemykh geodezicheskikh potokakh na gruppe dvizhenii evklidova prostranstva”, Nekotorye voprosy matematiki i mekhaniki, MGU, M., 1983, 8–9

[19] “Dinamicheskie sistemy na orbitakh lineinykh predstavlenii grupp Li i polnaya integriruemost nekotorykh gidrodinamicheskikh sistem”, Funkts. anal. i ego prilozh., 17:1 (1983), 31–39 (with A. T. Fomenko) | MR | Zbl

[20] “Kommutativnye graduirovannye algebry s dvoistvennostyu Puankare i gamiltonovy sistemy”, Topologicheskie i geometricheskie metody v matematicheskoi fizike, Izd-vo Voronezh. un-ta, Voronezh, 1983, 128–132 | MR

[21] “Rasshireniya algebr Li i gamiltonovy sistemy”, Izv. AN SSSR. Ser. mat., 47:6 (1983), 1303–1321 | MR | Zbl

[22] “Metodika postroeniya $S$-predstavlenii”, Vestn. MGU. Ser. 1. Mat., mekh., 1 (1984), 3–9

[23] “Integriruemost po Liuvillyu gamiltonovykh sistem na algebrakh Li”, Usp. mat. nauk, 39:2 (1984), 3–56 (with A. T. Fomenko) | MR | Zbl

[24] “Teoretiko-gruppovaya interpretatsiya nekotorykh klassov uravnenii klassicheskoi mekhaniki”, Differentsialnye uravneniya i ikh prilozheniya, MGU, M., 1984, 106–111

[25] “Zadacha Neimana i vpolne integriruemye geodezicheskie potoki na proektivnom prostranstve”, Funktsionalnyi analiz i ego prilozheniya v mekhanike i teorii veroyatnostei, MGU, M., 1984, 160–162

[26] “Simplekticheskie struktury na gruppakh avtomorfizmov simmetricheskikh prostranstv”, Vestn. MGU. Ser. 1, 6 (1984), 31–33

[27] Algebra, Metodicheskaya razrabotka dlya desyatykh klassov vechernego otdeleniya MMMF, Izd-vo MGU, 1984 (with L. P. Isupovym), 35 pp.

[28] “Novyi metod postroeniya vpolne integriruemykh gamiltonovykh sistem”, Kachestvennaya teoriya differentsialnykh uravnenii i teoriya upravleniya dvizheniem, Mezhvuzovskii sb. nauchnykh trudov, Izd-vo Mordovskogo gos. un-ta, Saransk, 1985, 35–39

[29] “Pamyati Petra Konstantinovicha Rashevskogo (1907–1983)”, Tr. semin. po vektor. i tenzor. anal., no. 22, 1985, 4–5 (with O. V. Manturovym, S. P. Novikovym, L. V. Sabininym, A. T. Fomenko)

[30] “Nauchno-issledovatelskii seminar po vektornomu i tenzornomu analizu i ego prilozheniyam”, Tr. semin. po vektor. i tenzor. anal., no. 22, 1985, 6–7 (with O. V. Manturovym, S. P. Novikovym, L. V. Sabininym, A. T. Fomenko)

[31] “Ploskie simmetricheskie prostranstva s nekompaktnymi gruppami dvizhenii i gamiltonovy sistemy”, Tr. semin. po vektor. i tenzor. anal., no. 22, 1985, 162–174 | Zbl

[32] Geometriya. Nachala analiza, Metodicheskaya razrabotka dlya desyatykh klassov vechernego otdeleniya MMMF, Izd-vo MGU, 1985 (with L. P. Isupovym), 34 pp.

[33] “Tsarevna Didona, izoperimetry i mylnye plenki”, Kvant, 1985, no. 5, 22–27

[34] “Kompyuternaya geometriya”, Metodicheskie rekomendatsii ministerstva prosvescheniya SSSR, 1986, 17–35

[35] “Deformatsii integriruemykh sistem”, Analiz na mnogoobraziyakh i differentsialnye uravneniya, Izd-vo Voronezh. un-ta, Voronezh, 1986, 156–164 | MR

[36] “Teoretiko-gruppovaya kharakteristika maksimalnogo pokazatelya kompaktnoi gruppy”, Geometriya, differentsialnye uravneniya i mekhanika, MGU, M., 1986, 135–139.

[37] “Geometriya skobok Puassona i metody integrirovaniya po Liuvillyu sistem na simmetricheskikh prostranstvakh”, Sovr. problemy matematiki. Noveishie dostizheniya. Itogi nauki i tekhniki, 29, VINITI, M., 1986, 3–108 (with A. T. Fomenko)

[38] “On the geometric properties of the commutative set of functions on symplectic manifold”, Bakinskaya mezhdunarodnaya topologicheskaya konf., Tez. dokl., ch. 2 (Baku, 3–9 oktyabrya, 1987), Baku, 1987, 297

[39] “Geometricheskie i algebraicheskie mekhanizmy integriruemosti gamiltonovykh sistem na odnorodnykh prostranstvakh i algebrakh Li”, Sovremennye probl. matematiki. Fundamentalnye napravleniya. Itogi nauki i tekhniki, 16, VINITI, M., 1987, 227–299 (with A. T. Fomenko)

[40] “Geometricheskie invarianty vpolne integriruemykh gamiltonovykh sistem”, Vses. konf. po geometrii “v tselom”, Novosibirsk, 1987, 121

[41] Tozhdestvennye preobrazovaniya. Planimetriya, MGU, 1987 (with V. A. Trofimovym)

[42] Izbrannye zadachi. Topologiya i algebra, MGU, 1987

[43] Integrable systems on Lie algebras and symmetric spaces, Gordon and Breach science publishers, 1988 (with A. T. Fomenko) | MR | Zbl

[44] “Obobschennye klassy Maslova lagranzhevykh poverkhnostei v simplekticheskikh mnogoobraziyakh”, Usp. mat. nauk, 43:4 (1988), 169–170

[45] “Indeks Maslova lagranzhevykh podmnogoobrazii simplekticheskikh mnogoobrazii”, Tr. semin. po vektor. i tenzor. anal., no. 23, 1988, 190–194 | Zbl

[46] “O gipoteze Fomenko dlya vpolne geodezicheskikh podmnogoobrazii s pochti kelerovoi metrikoi”, Izbrannye voprosy algebry, geometrii i diskretnoi matematiki, MGU, M., 1988, 122–123

[47] “Simplekticheskie svyaznosti, indeks Maslova i gipoteza Fomenko”, Dokl. AN SSSR, 304:6 (1989), 1302–1305 | Zbl

[48] “On the connections on symplectic manifolds and the topological invariants of Hamiltonian systems on Lie algebras”, Mezhdunar. konf. po algebre, Novosibirsk, 1989, 102

[49] “Geometricheskie invarianty lagranzhevykh sloenii”, Usp. mat. nauk, 44:4 (1989), 213

[50] “O geometricheskikh svoistvakh polnogo involyutivnogo semeistva funktsii na simplekticheskom mnogoobrazii”, Tr. mezhdunar. topologicheskoi konf., Baku, 1989, 173–184

[51] Vvedenie v geometriyu mnogoobrazii s simmetriyami, MGU, M., 1989 | Zbl

[52] Zadachi po teorii grupp Li i algebr Li, MGU, M., 1990

[53] Vektornyi analiz v krivolineinykh koordinatakh, Razdatochnyi material, MGTU, 1990 (with I. K. Babenko, E. V. Troitskim)

[54] “Connections on manifolds and new characteristic classes”, Acta Appl. Math., 22 (1991), 283–312 | DOI | MR | Zbl

[55] “Gruppa golonomii i obobschennye klassy Maslova podmnogoobrazii v prostranstvakh affinnoi svyaznosti”, Mat. zametki, 49:2 (1991), 113–123 | Zbl

[56] “Indeks Maslova v psevdorimanovoi geometrii”, Algebra, geometriya i diskretnaya matematika v nelineinykh zadachakh, MGU, 1991, 198–203

[57] “Symplectic connections and Maslov–Arnold characteristic classes”, Adv. Sov. Math., 6 (1991), 257–265 | MR | Zbl

[58] “Kompyuternye vychisleniya v geometricheskikh zadachakh SAPR”, Tr. semin. po vektor. i tenzor. anal., no. 4, 1991, 70–80 (with A. O. Ivanovym, A. A. Tuzhilinym, A. T. Fomenko)

[59] “Obobschennye indeksy Maslova i kobordizmy”, Tr. semin. po vektor. i tenzor. anal., no. 24, 1991, 186–198

[60] “Obobschennye klassy Maslova lagranzhevykh podmnogoobrazii”, Novoe v globalnom analize, Voronezh, 1991, 156–160

[61] “Connections on symplectic manifolds and characteristic classes of Hamiltonian systems”, Mathematical Physics, X, Springer-Verlag, 1992, 262–264 | MR

[62] “Ploskaya psevdorimanova struktura na kasatelnom rassloenii ploskogo mnogoobraziya”, Usp. mat. nauk, 47:3 (1992), 177–178 | MR

[63] “Prostranstvo putei i obobschennye klassy Maslova lagranzhevykh podmnogoobrazii”, Usp. mat. nauk, 47:4 (1992), 213–214 | MR

[64] “Psevdoevklidova struktura indeksa nol na kasatelnom rassloenii ploskogo mnogoobraziya”, Izbrannye voprosy algebry, geometrii i diskretnoi matematiki, MGU, 1992, 158–162

[65] “O svyaznostyakh absolyutnogo parallelizma na simplekticheskom mnogoobrazii”, Usp. mat. nauk, 48:1 (1993), 191–192

[66] “Otnositelnyi simplekticheskii ob'em na orbitakh koprisoedinennogo predstavleniya prostykh grupp Li”, Usp. mat. nauk, 48:6 (1993), 173–174

[67] “Nereshennye problemy v teorii topologicheskoi klassifikatsii integriruemykh gamiltonovykh sistem”, Tr. semin. po vektor. i tenzor. anal., no. 25(1), 1993, 6–16 (with A. V. Bolsinovym, A. T. Fomenko)

[68] “Kobordizmy mnogoobrazii affinnoi svyaznosti”, Tr. semin. po vektor. i tenzor. anal., no. 25(2), 1993, 142–147

[69] “Postroenie kanonicheskikh koordinat na orbitakh koprisoedinennogo predstavleniya grupp Li”, Tr. semin. po vektor. i tenzor. anal., no. 25(2), 1993, 148–151

[70] Geometricheskie invarianty integriruemykh gamiltonovykh sistem, Dissertatsiya na soiskanie uchenoi stepeni d.f.-m.n., MGU, 1993

[71] “Kanonicheskie koordinaty na orbitakh koprisoedinennogo predstavleniya tenzornykh rasshirenii grupp Li”, Usp. mat. nauk, 49:1 (1994), 229–230

[72] “Obobschennye klassy Maslova na prostranstve putei”, Tr. mat. in-ta im. V. A. Steklova, 205, 1994, 172–199 | Zbl

[73] “Introduction to geometry of manifolds with symmetry”, Math. and Its Applications, 270, Kluwer Academic Publ., Dordrecht–Boston–London, 1994 | MR

[74] Algebra i geometriya integriruemykh gamiltonovykh differentsialnykh uravnenii, Faktorial, Izd-vo Udmurtskogo gos. un-ta, M., 1995 (with A. T. Fomenko), 446 pp. | MR | Zbl

[75] Cordero L. A., Dodson T. J., de Leon M., Differential geometry of frame bundles, Kluwer Academic Publ., Dordrecht–Boston–London, 1989, 244 pp. ; Acta Appl. Math., 25 (1995), 195–199 | MR | Zbl

[76] “On the topology of the path space for a symplectic manifold”, Topology and Applications, Int. conf. dedicated to P. S. Alexandroff's 100th birthday (Moscow, May 27–31, 1996), Phasis, Moscow, 1996, 161–162

[77] “Nelineinaya ekonomicheskaya dinamika”, Fundam. prikl. mat., 3:2 (1997), 319–349 (with Z. G. Psioloi i E. R. Rozendornom) | MR

[78] Preface to: F. T. Fomenko, O. V. Manturov, V. V. Trofimov, Tensor and vector analysis. Geometry, mechanics and physics, Gordon and Breach, London, 1998, xi–xii (with A. T. Fomenko, O. V. Manturovym) | MR

[79] “Variatsionnye zadachi v modeli finansovykh potokov”, Topologicheskie metody v teorii gamiltonovykh sistem, eds. A. V. Bolsinov, A. T. Fomenko, A. I. Shafarevich, Faktorial, M., 1998, 315–320