minimal surfaces,
Plateau problem,
topology and geometry of Lie groups,
homogeneous spaces,
dynamical systems,
integrable Hamiltonian equations,
topological invariants of dynamical systems,
computer geometry,
topology of three-dimensional manifolds,
Hamiltonian mechanics,
symplectic geometry.
Subject:
In the theory of minimal surfaces was proved the multidimensional Plateau problem in the class of spectral bordisms of Riemannian manifolds. Then, as application of this general construction, was proved the global minimality of many well-known submanifolds in homogeneous Riemannian spaces of compact Lie groups. New scientific branch was developed, namely, the theory of topological classification of nondegenerate Hamiltonian differential equations (dynamical systems) of general type. New topological invariants, describing the topological type of singularities of dynamical systems, were discovered. As a result, was obtained the classification of integrable Hamiltonian systems with two degrees of freedom, up to Liouville equivalence and up to orbital equivalence (of topological and smooth type).
Biography
Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1967 (department of differential geometry). Ph. D. thesis was defended in 1970. D. Sci. thesis was defended in 1972. A list of my mathematical works contains more than 180 titles. A list of my books in mathematics contains 30 titles. Since 1980 I have led the research seminar "Modern Geometrical Methods" at MSU (Department of Mathematics and Mechanics).
Award of Moscow Mathematical Society, 1974. Award of the Presidium of Academy of Science, USSR, 1987. State Award of Russian Federation, 1996.
Main publications:
Fomenko A. T., “Periodichnost Botta s tochki zreniya mnogomernogo funktsionala Dirikhle”, Izv. AN SSSR. Ser. matem., 35:3 (1971), 667–681
Fomenko A. T., “Mnogomernaya zadacha Plato v rimanovykh mnogoobraziyakh”, Matem. sb., 89:3 (1972), 475–519
Mischenko A. S., Fomenko A. T., “Obobschennyi metod Liuvillya integrirovaniya gamiltonovykh sistem”, Funkts. analiz i ego prilozh., 12:2 (1978), 46–56
Fomenko A. T., “Teoriya Morsa integriruemykh gamiltonovykh sistem”, Dokl. AN SSSR, 287:5 (1986), 1071–1075
G. V. Belozerov, A. T. Fomenko, “Orbital invariants of noncompact integrable systems with two degrees of freedom”, Moscow University Mathematics Bulletin, 80:2 (2025), 136–141
2.
G.V. Belozerov, A.T. Fomenko, “Skrytye simmetrii v gamiltonovoi geometrii, topologii, fizike i mekhanike”, Priroda, 2025, no. 1, 23–29
2024
3.
G. V. Belozerov, A. T. Fomenko, “Orbital invariants of billiards and linearly integrable geodesic flows”, Sb. Math., 215:5 (2024), 573–611
4.
G. V. Belozerov, A. T. Fomenko, “Generalized Jacobi–Chasles theorem in non-Euclidean spaces”, Sb. Math., 215:9 (2024), 1159–1181
5.
G. V. Belozerov, A. T. Fomenko, “Rotation functions of integrable billiards as orbital invariants”, Dokl. Math., 109:1 (2024), 1–5
6.
A. T. Fomenko, A. I. Shafarevich, V. A. Kibkalo, “Main recent directions and achievments of the Chair of Differential Geometry and Applications”, Moscow University Mathematics Bulletin, 79:6 (2024), 283–295
K.V. Shaitan, A.K. Shaitan, G.M. Kobelkov, A.T. Fomenko, M.P. Kirpichnikov, “Matematika v biologii - gde tochki rosta?”, Mezhdunarodnaya konferentsiya «Matematika v sozvezdii nauk». K yubileyu rektora MGU akademika Viktora Antonovicha Sadovnichego. Tezisy dokladov (Moskva, 1–2 aprelya 2024 g.), Izdatelstvo Moskovskogo universiteta, Moskva, 2024, 790–791 (to appear)
9.
S.V. Matveev, A.T. Fomenko, Algoritmicheskie i kompyuternye metody v trekhmernoi topologii, Trudy vydayuschikhsya uchenykh MGU, 2-e izdanie, ispravlennoe, Izdatelstvo Moskovskogo universiteta, Moskva, 2024, 302 pp.
10.
S. O. Gorchinskiy, V. G. Danilov, S. Yu. Dobrokhotov, V. V. Kozlov, V. E. Nazaikinskii, N. N. Nefedov, D. O. Orlov, S. A. Stepin, I. A. Taimanov, D. V. Treschev, N. A. Tyurin, A. T. Fomenko, S. E. Yakush, “Andrei Igorevich Shafarevich (on his sixtieth birthday)”, Russian Math. Surveys, 79:3 (2024), 553–556
A.T. Fomenko, “Billiards of Variable Configuration and Billiards With Slipping
in Hamiltonian Geometry and Topology”, Lobachevskii Journal of Mathematics, 44:10 (2023), 4512–4522
14.
A. T. Fomenko, V. V. Vedyushkina, “Billiards and integrable systems”, Russian Math. Surveys, 78:5 (2023), 881–954
15.
A.T. Fomenko, Variatsionnye metody v topologii, Trudy vydayuschikhsya uchenykh MGU, 2-e izdanie, ispravlennoe, Izd-vo Moskovskogo un-ta, Moskva, 2023, 343 pp.
A. T. Fomenko, V. V. Vedyushkina, “Evolutionary force billiards”, Izv. Math., 86:5 (2022), 943–979
18.
A. T. Fomenko, “Billiardy peremennoi konfiguratsii v gamiltonovoi
geometrii i topologii”, Mezhdunarodnaya konferentsiya “Lobachevskie chteniya”. Sbornik trudov. (Kazan, 30 iyunya - 4 iyulya 2022 g.), Trudy Matematicheskogo tsentra imeni N.I.Lobachevskogo, 62, Regionalnyi nauchno-obrazovatelnyi matematicheskii tsentr PFO, Kazan, 2022, 112–115
19.
A. T. Fomenko, V. A. Kibkalo, “Topology of Liouville foliations of integrable billiards on table-complexes”, European Journal of Mathematics, 8 (2022), 1392–1423
A.T. Fomenko, Simplekticheskaya geometriya. Metody i prilozheniya., 2-e izd., URSS, Moskva, 2022, 408 pp.
21.
A. A. Tuzhilin, A. T. Fomenko, Elementy geometrii i topologii minimalnykh poverkhnostei, 2-e izd., stereotipnoe, URSS, Moskva, 2022, 256 pp.
22.
A. T. Fomenko, Matematika, Mif, “Master i Margarita” v 199 kartinakh: smykaya vershiny ratsionalnogo myshleniya s glubinami arkhaicheskogo i bessoznatelnogo, URSS, Moskva, 2022, 424 pp.
23.
V. V. Aleksandrov, S. B. Gashkov, D. V. Georgievskii, O. S. Dudakova, V. P. Karlikov, B. S. Kashin, G. M. Kobel'kov, M. D. Kovalev, V. V. Kozlov, R. M. Kolpakov, V. V. Kochergin, T. P. Lukashenko, A. S. Mishchenko, Yu. V. Nesterenko, R. I. Nigmatulin, N. P. Red'kin, V. A. Sadovnichii, I. N. Sergeev, A. T. Fomenko, A. V. Chashkin, V. N. Chubarikov, A. I. Shafarevich, A. N. Shiryaev, V. Ya. Shkadov, A. A. Shkalikov, “90 years since the birthday of Academician Oleg Borisovich Lupanov (02.06.1932 – 03.05.2006)”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2022, no. 3, 3–5
A. I. Shafarevich, A. T. Fomenko, V. N. Chubarikov, A. O. Ivanov, V. G. Chirskii, V. I. Bernik, V. A. Bykovskii, A. I. Galochkin, S. S. Demidov, S. B. Gashkov, A. I. Nizhnikov, A. A. Fomin, E. Deza, A. Ya. Kanel-Belov, N. M. Dobrovolsky, N. N. Dobrovolsky, I. Yu. Rebrova, V. Kh. Salikhov, “Yuri Valentinovich Nesterenko (to the 75th anniversary)”, Chebyshevskii Sb., 23:1 (2022), 10–20
2021
26.
A.T. Fomenko, V.A. Kibkalo, “Saddle Singularities in Integrable Hamiltonian Systems: Examples and Algorithms”, Contemporary Approaches and Methods in Fundamental Mathematics and Mechanics, Understanding Complex Systems, eds. Sadovnichiy V.A., Zgurovsky M.Z., Springer, 2021, 3-26
V. A. Kibkalo, A. T. Fomenko, I. S. Kharcheva, “Realizing integrable Hamiltonian systems by means of billiard books”, Trans. Moscow Math. Soc., 82 (2021), 37–64
30.
Fomenko, A.T., Vedyushkina, V.V., “Billiards with Changing Geometry and Their Connection with the Implementation of the Zhukovsky and Kovalevskaya Cases”, Russ. J. Math. Phys., 28 (2021), 317-332
V. V. Vedyushkina, A. T. Fomenko, “Force evolutionary billiards and billiard equivalence of the Euler and Lagrange cases”, Dokl. Math., 103:1 (2021), 1–4
32.
S. B. Gashkov, O. S. Dudakova, M. D. Kovalev, R. M. Kolpakov, V. V. Kochergin, N. P. Red'kin, A. T. Fomenko, A. V. Chashkin, V. N. Chubarikov, A. I. Shafarevich, A. D. Yashunskii, “Oktay Muradovińh Kasim-Zade (29.04.1953–22.12.2020)”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2021, no. 4, 60–63
33.
Dubrovin B.A., Novikov S.P., Fomenko A.T., Sovremennaya geometriya: Metody i prilozheniya: Geometriya i topologiya mnogoobrazii, v. 2, 7-e izd., URSS, 2021
34.
V. V. Aleksandrov, S. B. Gashkov, D. V. Georgievskii, V. P. Karlikov, B. S. Kashin, G. M. Kobel'kov, V. V. Kozlov, T. P. Lukashenko, A. S. Mishchenko, Yu. V. Nesterenko, R. I. Nigmatulin, O. V. Popov, V. A. Sadovnichii, I. N. Sergeev, G. V. Fedorov, A. T. Fomenko, A. I. Shafarevich, A. N. Shiryaev, V. Ya. Shkadov, A. A. Shkalikov, “To 70-th anniversary of professor V. N. Chubarikov”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2021, no. 5, 69–71
35.
A. I. Shafarevich, A. T. Fomenko, A. O. Ivanov, S. S. Demidov, S. B. Gashkov, A. I. Nizhnikov, A. A. Fomin, E. Deza, A. Ya. Kanel-Belov, N. M. Dobrovol'skii, N. N. Dobrovol'skii, I. Yu. Rebrova, “Vladimir Nikolaevich Chubarikov (to the 70th anniversary of his birth)”, Chebyshevskii Sb., 22:5 (2021), 5–15
2020
36.
D. A. Fedoseev, A. T. Fomenko, “Noncompact Bifurcations of Integrable Dynamic Systems”, Journal of Mathematical Sciences, 248 (2020), 810–827
V. V. Vedyushkina, V. A. Kibkalo, A. T. Fomenko, “Topological Modeling of Integrable Systems by Billiards: Realization of Numerical Invariants”, Doklady Mathematics, 102:1 (2020), 269–271
38.
A. S. Mischenko, A. T. Fomenko, Kurs differentsialnoi geometrii i topologii, 4-e izd., pererab. i dop., URSS, Moskva, 2020, 504 pp.
2019
39.
A. T. Fomenko, K. I. Solodskih, “Three-Dimensional Manifolds of Constant Energy and Invariants of Integrable Hamiltonian Systems”, Modern Mathematics and Mechanics. Fundamentals, Problems and Challenges, Understanding Complex Systems, eds. V. A. Sadovnichiy, M. Z. Zgurovsky, Springer, 2019, 13–30
40.
V. V. Vedyushkina (Fokicheva), A. T. Fomenko, “Integrable geodesic flows on orientable two-dimensional surfaces and topological billiards”, Izv. Math., 83:6 (2019), 1137–1173
41.
A. T. Fomenko, V. V. Vedyushkina, “Billiards and integrability in geometry and physics. New scope and new potential”, Moscow University Mathematics Bulletin, 74:3 (2019), 98–107
42.
A. T. Fomenko, V. V. Vedyushkina, “Singularities of integrable Liouville systems, reduction of integrals to lower degree and topological billiards: recent results”, Theor. Appl. Mech., 46:1 (2019), 47–63
V. V. Vedyushkina, A. T. Fomenko, “Realizatsiya effektov sistem fiziki i mekhaniki integriruemymi billiardami”, Materialy konferentsii «Sovremennye problemy matematiki i mekhaniki», posvyaschennoi 80-letiyu akademika V.A.Sadovnichego (Moskva, 13–15 maya 2019 g.), MGU, 2019, 607–610
44.
A. T. Fomenko, “Billiards and Integrability”, Abstracts. International Conference on Finite Dimensional Integrable Systems in Geometry and Mathematical Physics (Shanghai, China, 2019, May 6–12), Shanghai Jiao Tong University, 2019, 11–13
45.
V. V. Vedyushkina, A. T. Fomenko, “Ponizhenie stepeni integralov gamiltonovykh sistem s pomoschyu billiardov”, Doklady Akademii nauk, 486:2 (2019), 151–155
A. T. Fomenko and V. V. Vedyushkina, “Topological billiards, conservation laws and classification of trajectories”, Functional Analysis and Geometry: Selim Grigorievich Krein Centennial, Contemporary Mathematics, 733, eds. Peter Kuchment and Evgeny Semenov, American Mathematical Society, 2019, 129–148
A. T. Fomenko, V. V. Vedyushkina, “Implementation of integrable systems by topological, geodesic billiards with potential and magnetic field”, Russian Journal of mathematical physics, 26:3 (2019), 320–333
A. T. Fomenko, Differentsialnaya geometriya i topologiya. Dopolnitelnye glavy, Klassicheskii uchebnik MGU, 3-e izd., ispr. i dop., LELAND, URSS, Moskva, 2019, 304 pp.
49.
A. T. Fomenko, Topologicheskie variatsionnye zadachi, Klassicheskii uchebnik MGU, 2-e izd., ispr. i dop., LELAND, URSS, Moskva, 2019, 336 pp.
2018
50.
V. V. Vedyushkina, A. T. Fomenko, “Nevypuklye topologicheskie billiardy kak modeli integriruemykh geodezicheskikh potokov na orientiruemykh poverkhnostyakh”, Materialy Mezhdunarodnoi Konferentsii «Voronezhskaya zimnyaya matematicheskaya shkola S.G. Kreina – 2018», izdatelsko-poligraficheskii tsentr «Nauchnaya kniga», Voronezh, 2018, 348–352
51.
V. V. Vedyushkina, A. T. Fomenko, I. S. Kharcheva, “Modeling nondegenerate bifurcations of closures of solutions for integrable systems with two degrees of freedom by integrable topological billiards”, Dokl. Math., 97:2 (2018), 174–176
52.
A. T. Fomenko, “Topological billiards and integrable Hamiltonian systems”, International Conference on Partial Differential Equations and Applications in Memory of Professor B.Yu.Sternin (Moskva, 6–9 noyabrya 2018), RUDN, 2018, 30–31
53.
V. M. Buchstaber, V. A. Vassiliev, A. Yu. Vesnin, I. A. Dynnikov, Yu. G. Reshetnyak, A. B. Sossinsky, I. A. Taimanov, V. G. Turaev, A. T. Fomenko, E. A. Fominykh, A. V. Chernavsky, “Sergei Vladimirovich Matveev (on his 70th birthday)”, Russian Math. Surveys, 73:4 (2018), 737–746
54.
A. T. Fomenko, Naglyadnaya geometriya i topologiya. Matematicheskie obrazy v realnom mire, 3-e izd., ispr. i dop., URSS, 2018, 480 pp.
2017
55.
V. V. Vedyushkina (Fokicheva), A. T. Fomenko, “Integrable topological billiards and equivalent dynamical systems”, Izv. Math., 81:4 (2017), 688–733
56.
V. V. Vedyushkina, A. O. Ivanov, A .A. Tuzhilin, A. T. Fomenko, “Kompyuternye modeli v geometrii i dinamike”, Intellektualnye sistemy. Teoriya i prilozheniya, 20:1 (2017), 8, 20 pp. http://intsysjournal.ru/articles/is2101/docklad_ffit.pdf
57.
V. V. Vedyushkina, A. O. Ivanov, A. A. Tuzhilin, A. T. Fomenko, Intelligent systems, 21:1 (2017), 164–191
58.
V. N. Chubarikov, A. T. Fomenko, S. S. Demidov, V. N. Chinenova, “Irina Alexandrovna Tulina is 95”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2017, no. 5, 70–71
2016
59.
A. T. Fomenko, V. V. Fokicheva, S. S. Nikolaenko, “Topologicheski ekvivalentnye sluchai integriruemosti v dinamike”, Materialy mezhdunarodnoi konferentsii «Voronezhskaya zimnyaya matematicheskaya shkola S. G. Kreina-2016», Izdatelsko-poligraficheskii tsentr «Nauchnaya kniga», Voronezh, 2016, 407–417
60.
A. T. Fomenko, “Topologicheskie billiardy s bogatymi simmetriyami modeliruyut vazhnye sluchai gamiltonovoi dinamiki v fizike i mekhanike”, Materialy mezhdunarodnoi konferentsii po algebre, analizu i geometrii (Kazan, 25 iyunya – 4 iyulya 2016 g.), Kazanskii federalnyi universitet, 2016, 35
61.
A. Fomenko, D. Fuchs, Homotopical Topology, Graduate Texts in Mathematics, 273, 2nd edition, Springer, 2016, 627 pp.
V. V. Fokicheva and A. T. Fomenko, “Billiard systems as the models for the rigid body dynamics”, Studies in Systems, Decision and Control, Advances in Dynamical Systems and Control, 69, eds. V. A. Sadovnichiy, M. Z. Zgurovsky, Springer International Publishing, 2016, 13–32
D. A. Fedoseev, A. T. Fomenko, “Noncompact bifurcations of integrable dynamic systems”, J. Math. Sci., 248:6 (2020), 810–827
2016
64.
A. S. Mischenko, Yu. P. Solovev, A. T. Fomenko, Sbornik zadach po differentsialnoi geometrii i topologii, URSS, Moskva, 2016, 416 pp.
2015
65.
A. T. Fomenko, V. V. Fokicheva, “Integrable billiards model important integrable cases of rigid body dynamics”, Doklady Mathematics, 92:3 (2015), 682–684
66.
A. T. Fomenko, S. S. Nikolaenko, “The Chaplygin case in dynamics of a rigid body in fluid is orbitally equivalent to the Euler case in rigid body dynamics and to the Jacobi problem about geodesics on the ellipsoid”, Journal of Geometry and Physics, 87 (2015), 115–133
A. T. Fomenko, E. O. Kantonistova, “Topological Classification of Geodesic Flows on Revolution 2-Surfaces with Potential”, Continuous and Distributed Systems II. Theory and Applications, Studies in Systems, Decision and Control, 30, Springer, 2015, 11–17
2014
68.
A. T. Fomenko, A. Yu. Konyaev, “Algebra and Geometry Through Hamiltonian Systems”, Continuous and Distributed Systems. Theory and Applications, Solid Mechanics and Its Applications, 221, eds. V. Z. Zgurovsky, V. A. Sadovnichiy, Springer, 2014, 3–21
A.T.Fomenko, “Topological classification of integrable systems and billiards in confocal quadrics”, Book of Abstracts. International Conference. 13th Serbian Mathematical Congress. (Vrnjacka Banja, Serbia, May 22–25, 2014), Mathematical Society of Serbia, Belgrade, Serbia, 2014, 82
71.
A.T.Fomenko, “Topology of Integrable Hamiltonian Systems - Recent Results”, Book of Abstracts. International Conference. 13th Serbian Mathematical Congress (Vrnjacka Banja, Serbia, May 22-25, 2014), Mathematical Society of Serbia, Belgrade, Serbia, 2014, 83
72.
A.T.Fomenko, “Topological classification of integrable systems and billiards in confocal quadrics”, Book of Abstracts. XVIII Geometrical Seminar (Vrnjacka Banja, Serbia, May 25-28, 2014), Faculty of Sciences and Mathematics, University of Nis, Serbia, 2014, 38–39
73.
V. A. Sadovnichii , V. N. Chubarikov, V. I. Gavrilov, T. P. Lukashenko, A. T. Fomenko, I. Kh. Sabitov, A. K. Rybnikov, “Pamyati Leonida Evgenevicha Evtushika (25.05. 1931 - 16.02.2013)”, Vestnik Moskovskogo universiteta. Seriya 1: Matematika. Mekhanika, 2014, no. 5, 69–70
74.
A.A.Tuzhilin, A.T.Fomenko, Elementy geometrii i topologii minimalnykh poverkhnostei, Klassicheskii uchebnik MGU, izdanie vtoroe, dopolnennoe, URSS, 2014
V.V.Aleksandrov, V.P.Karlikov, V.E.Podolskii, A.T.Fomenko, V.N.Chubarikov, A.A.Shkalikov, “Akademik Viktor Antonovich Sadovnichii”, Vestnik MGU, seriya matematika, mekhanika, 2014, 3–5
77.
A.A.Oshemkov, F.Yu.Popelenskii, A.A.Tuzhilin, A.T.Fomenko, A.I.Shafarevich, Kurs naglyadnoi geometrii i topologii, Klassicheskii uchebnik MGU, Lenand, Moskva, 2014, 360 pp.
78.
A. I. Aptekarev, P. A. Borodin, B. S. Kashin, Yu. V. Nesterenko, P. V. Paramonov, A. V. Pokrovskii, A. G. Sergeev, A. T. Fomenko, “Evgenii Prokof'evich Dolzhenko (on his 80th birthday)”, Russian Math. Surveys, 69:6 (2014), 1143–1148
2013
79.
A.T.Fomenko, E.A.Kudryavtseva, “Each finite group is a symmetry group of some map (an "atom"-bifurcation)”, Moscow Univ. Math. Bull., 68:3 (2013), 148–155
2012
80.
F. S. Avdeev, G. I. Arkhipov, S. B. Gashkov, N. M. Dobrovol'skii, B. S. Kashin, I. I. Mel'nikov, M. P. Mineev, Yu. V. Nesterenko, S. M. Nikol'skii, A. N. Parshin, V. P. Platonov, Yu. V. Prokhorov, V. A. Sadovnichii, A. T. Fomenko, V. G. Chirskii, “Vladimir Nikolaevich Chubarikov (on his 60th birthday)”, Russian Math. Surveys, 67:1 (2012), 189–193
2013
81.
B.A.Dubrovin, S.P.Novikov, A.T.Fomenko, Sovremennaya geometriya. Metody i prilozheniya, v. 1, Klassicheskii universitetskii uchebnik. Moskovskii gosudarstvennyi universitet im.M.V.Lomonosova, Geometriya poverkhnostei, grupp preobrazovanii i polei, Izdanie shestoe, izd-vo URRS, knizhnyi dom “Librokom”, Moskva, 2013
82.
B.A.Dubrovin, S.P.Novikov, A.T.Fomenko, Sovremennaya geometriya. Metody i prilozheniya, v. 2, Klassicheskii universitetskii uchebnik. Moskovskii gosudarstvennyi universitet im.M.V.Lomonosova, Geometriya i topologiya mnogoobrazii, Izdanie shestoe, izd-vo URRS, knizhnyi dom “Librokom”, Moskva, 2013
83.
B.A.Dubrovin, S.P.Novikov, A.T.Fomenko, Sovremennaya geometriya. Metody i prilozheniya, v. 3, Klassicheskii universitetskii uchebnik. Moskovskii gosudarstvennyi universitet im.M.V.Lomonosova, Teoriya gomologii, Izdanie shestoe, izd-vo URRS, knizhnyi dom “Librokom”, Moskva, 2013
84.
A.T.Fomenko, A.S.Mishchenko, Yu.P.Solovyev, Selected Problems in Differential Geometry and Topology, Cambridge Scientific Publishers, 2013
85.
V. N. Chubarikov, A. T. Fomenko, A. S. Mishchenko, E. V. Shchepin, B. A. Pasynkov, V. I. Ponomarev, S. D. Iliadis, Yu. V. Sadovnichii, K. L. Kozlov, “Vitalii Vital'evich Fedorchuk (01.11.1942 – 09.12.2012)”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2013, no. 4, 70–71
A.T.Fomenko, A.Yu.Konyaev, “New approach to symmetries and singularities in integrable Hamiltonian systems”, Topology and its Applications, 159 (2012), 1964–1975
A.T.Fomenko, A.Yu.Konyaev, “New approach to symmetries and singularities in integrable Hamiltonian systems”, Topology and its Applications, 159 (2012), 1964–1975
E.A.Kudryavtseva, A.T.Fomenko, “Gruppy simmetrii pravilnykh funktsii Morsa na poverkhnostyakh”, Doklady RAN, seriya: matematika, 446:6 (2012), 615–617
90.
A.T.Fomenko, “Hidden Symmetries in Integrable Hamiltonian Systems”, Progress in Analysis. Proceedings of the 8th Congress of the International Society for Analysis, its Applications, and Computation, Volume 1, Peoples' Friendship University of Russia, Moscow, 2012, 26–41
91.
F. S. Avdeev, G. I. Arkhipov, S. B. Gashkov, N. M. Dobrovol'skii, B. S. Kashin, I. I. Mel'nikov, M. P. Mineev, Yu. V. Nesterenko, S. M. Nikol'skii, A. N. Parshin, V. P. Platonov, Yu. V. Prokhorov, V. A. Sadovnichii, A. T. Fomenko, V. G. Chirskii, “Vladimir Nikolaevich Chubarikov (on his 60th birthday)”, Russian Math. Surveys, 67:1 (2012), 189–193
2011
92.
A. T. Fomenko, “Hidden symmetries in integrable dynamical systems”, Abstracts. 8th International ISAAC Congress (Moscow, August 22-27, 2011), Peoples' Friendship University of Russia, Moscow, 2011, 36
Fomenko A.T., “Singularities and bifurcations of integrable Hamiltonian Systems”, Abstracts of 2010 International Conference on Topolody and its Applications (June 26–30 Nafpaktos, Greece), 2010, 98–99
Mischenko A.S., Fomenko A.T., Kurs differentsialnoi geometrii i topologii, izdanie trete, pererabotannoe i dopolnennoe, Izd-vo Lan, Sankt-Peterburg, Moskva, Krasnodar, 2010
97.
A. T. Fomenko, Nelin. Dinam., 6:4 (2010), 891–892
98.
I. V. Astashova, A. V. Borovskikh, V. V. Bykov, A. N. Vetokhin, V. V. Kozlov, V. A. Kondratiev, A. A. Kon'kov, N. Kh. Rozov, I. N. Sergeev, V. N. Chubarikov, A. T. Fomenko, A. S. Shamaev, “To memory of Vladimir Mikhailovich Millionshchikov”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2010, no. 2, 71–72
2009
99.
Fomenko A.T., Mishchenko A.S., A short course in differential geometry and topology, Cambridge Scientific Pub., Cambridge, UK, 2009, xi+273 pp.
100.
Kudryavtseva E.A., Nikonov I.M., Fomenko A.T. , “Simmetrichnye i neprivodimye abstraktnye mnogogranniki”, Matematika. Vypusk 2. Geometriya i topologiya, Sovremennye problemy matematiki i mekhaniki, Moskovskii gosudarstvennyi universitet im. M. V. Lomonosova, Moskva, 2009, 58–97
2011
101.
A. O. Ivanov, A. A. Tuzhilin, A. T. Fomenko, “Computer modeling of curves and surfaces”, J. Math. Sci., 172:5 (2011), 663–689
Nikonov I.M., Fomenko A.T., Shafarevich A.I., “K 75-letiyu konchiny Dmitriya Fedorovicha Egorova”, Istoriko-matematicheskie issledovaniya, vtoraya seriya, no. 13(48), Rossiiskaya Akademiya nauk, Institut istorii estestvoznaniya i tekhniki im. S. I. Vavilova, 2009, 49–53
2008
104.
E. A. Kudryavtseva, I. M. Nikonov, A. T. Fomenko, “Maximally symmetric cell decompositions of surfaces and their coverings”, Sb. Math., 199:9 (2008), 1263–1353
105.
Fomenko A.T., Shnurnikov I.N., “Retragiruemye spainy s odnoi dvumernoi kletkoi”, Tezisy dokladov. Voronezhskaya zimnyaya matematicheskaya shkola S. G. Kreina - 2008, Voronezhskii gos. un-t, Voronezh, 2008, 140–141
106.
Kudryavtseva E.A., Nikonov I.M., Fomenko A.T., “Maksimalno simmetrichnye kletochnye razbieniya poverkhnostei i ikh nakrytiya”, Mezhdunarodnaya konferentsiya “Differentsialnye uravneniya i topologiya”, posvyaschennaya 100-letiyu so dnya rozhdeniya Lva Semenovicha Pontryagina, Tezisy dokladov (Moskva, 17–22 iyunya 2008), Matematicheskii in-t im. V. A. Steklova RAN, Moskovskii gosudarstvennyi universitet im. M. V. Lomonosova, 2008, 471
107.
Fomenko A.T., Goldberg V.V., Kirichenko V.F., Lychagin V.V., Shelekhov A.M., “Maks A. Akivis”, J. Gen. Lie Theory Appl., 2:1 (2008), 1–18
108.
N. M. Bliznyakov, V. M. Buchstaber, Yu. E. Gliklikh, V. G. Zvyagin, A. S. Mishchenko, V. V. Obukhovskii, Yu. I. Sapronov, A. T. Fomenko, A. V. Chernavskii, “Yurii Grigor'evich Borisovich (obituary)”, Russian Math. Surveys, 63:4 (2008), 767–769
109.
Fomenko A.T., Goldberg V.V., Kirichenko V.F., Lychagin V.V., “Maks A. Akivis. On the occasion of his 85-th birthday and 65 years of scientific activity”, Maks A. Akivis. Selected Papers, Heldermann Verlag, Germany, 2008, xi-xx
Fomenko A.T., Korotkevich A.A., “Novye serii integriruemykh sistem na algebrakh Li”, Voronezhskaya zimnyaya Matematicheskaya shkola S. G. Kreina. Tezisy dokladov, Voronezhskii gos. un-t, Voronezh, 2006, 102
112.
Kalashnikov V.V., Nosovskii G.V., Fomenko A.T., Zvezdy. (Astronomicheskie metody v khronologii. Almagest Ptolemeya. Ptolemei. Tikho Brage. Kopernik. Egipetskie zodiaki), v. 1, Izd-vo RIMIS, Moskva, 2006
113.
Nosovskii G.V., Fomenko A.T., Fomenko T.N., Zvezdy. (Astronomicheskie metody v khronologii. Almagest Ptolemeya. Ptolemei. Tikho Brage. Kopernik. Egipetskie zodiaki), v. 2, Izd-vo RIMIS, Moskva, 2006
114.
Fomenko A.T., “Topology and geometry of integrable Hamiltonian systems on Lie algebras. New development”, International Conference on Topology and its Applications (June 23–26, 2006), Abstracts, Municipal Library of Aegon, Aegion, Greece, 2006, 68–69
115.
Bolsinov A.V., Fomenko A.T., Oshemkov A.A., Topological methods in the theory of integrable Hamiltonian systems, Cambridge Scientific Publishers, 2006
116.
Fomenko A.T., Fomenko T.N., “O topologicheskikh rabotakh A. N. Tikhonova. (K 100-letiyu so dnya rozhdeniya)”, Akademik Andrei Nikolaevich Tikhonov. K 100-letiyu so dnya rozhdeniya, Izd-vo MAKS-PRESS, Moskva, 2006, 109–115
117.
Golovanov N.N., Ilyutko D.P., Nosovskii G.V., Fomenko A.T., Kompyuternaya geometriya, Prikladnaya matematika i informatika, Izdatelskii tsentr “Akademiya”, Moskva, 2006
2004
118.
Fomenko A.T., Morozov P.V., “Some new results in topological classification of integrable systems in rigid body dynamics”, Contemporary geometry and related topics, World Sci. Publ., River Edge, NJ, 2004, 201–222
Mischenko A.S., Solovev Yu.P., Fomenko A.T., Sbornik zadach po differentsialnoi geometrii i topologii, pererabotannoe i dopolnennoe izdanie, Fizmatlit, Moskva, 2004
123.
Bokan N., Djoric M., Fomenko A.T., Rakic Z., Weiss J. (Eds.), Proceedings of the Workshop “Contemporary Geometry and Related Topics” (Belgrade, Yugoslavia, 15–21 May 2002), World Scientific Publishing Co., 2004
124.
V. V. Belokurov, A. A. Egorov, A. S. Mishchenko, F. Yu. Popelenskii, V. A. Sadovnichii, E. V. Troitskii, A. T. Fomenko, E. T. Shavgulidze, “Yurii Petrovich Solov'ev (obituary)”, Russian Math. Surveys, 59:5 (2004), 941–947
2003
125.
P. V. Morozov, A. T. Fomenko, “New results on topological classification of integrable systems in the mechanics of rigid body”, Tr. Geom. Semin., 24, Kazan Mathematical Society, Kazan, 2003, 107–120
Fomenko A.T., Hayat-Legrand C., Shafarevich A.I., “Topology of low-dimensional manifolds and geometry of Hamiltonian systems with applications to physics and mechanics”, French-Russian A. M. Liapunov Institute for Applied Mathematics and Computer Science. Transactions, 4, MGU, Moskva, 2003, 190–199
128.
Fomenko A.T., Ivanov A.A., Tuzhilin A.A., “Visual Topology and Variational Problems on Two-Dimensional Surfaces”, Mathematics and Culture. II. Visual Parfection: Mathematics and Creativity, ed. Michele Emmere, Springer Verlag, 2003, 99–123
2002
129.
Brailov Yury A., Fomenko Anatoly T., “Lie groups and integrable Hamiltonian systems”, Recent advances in Lie theory (Vigo, 2000), Res. Exp. Math., 25, Heldermann, Lemgo, 2002, 45–76
130.
V. V. Trofimov, A. T. Fomenko, “Riemannian geometry”, J. Math. Sci. (New York), 109:2 (2002), 1345–1501
131.
Fomenko A.T., Nosovskii G.V., “O “novgorodskikh datirovkakh” A. A. Zaliznyaka i V. L. Yanina”, Vestnik Rossiiskoi Akademii nauk, 72:2 (2002), 134–140
2001
132.
Fomenko A.T., Matematika i mif skvoz prizmu geometrii, Izd-vo Mosk. un-ta, M., 2001
133.
Mischenko A.S., Solovev Yu.P., Fomenko A.T., Sbornik zadach po differentsialnoi geometrii i topologii, Fizmatlit, M., 2001
134.
D. V. Anosov, A. A. Bolibrukh, A. M. Vershik, A. A. Gonchar, R. I. Grigorchuk, V. V. Kozlov, V. P. Maslov, E. F. Mishchenko, Ya. G. Sinai, V. M. Tikhomirov, P. L. Ul'yanov, A. T. Fomenko, “Anatolii Mikhailovich Stepin (on his 60th birthday)”, Russian Math. Surveys, 56:1 (2001), 201–205
135.
A. A. Irmatov, O. B. Lupanov, V. P. Maslov, V. M. Manuilov, A. A. Mikhalev, V. A. Sadovnichii, Yu. P. Solov'ev, E. V. Troitskii, A. T. Fomenko, “Aleksandr Sergeevitch Mischenko”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2001, no. 5, 67–69
2000
136.
Bolsinov A.V., Fomenko A.T., Integrable geodesic flows on two-dimensional surfaces, Monographs in Contemporary Mathematics, Consultants Bureau, New York, 2000, xiv+322 pp.
137.
Fomenko A., “Minimal surfaces”, Quantum, 10:5 (2000), 4–7
138.
A. V. Bolsinov, P. H. Richter, A. T. Fomenko, “The method of loop molecules and the topology of the Kovalevskaya top”, Sb. Math., 191:2 (2000), 151–188
139.
Mischenko A.S., Fomenko A.T., Kurs differentsialnoi geometrii i topologii, izdanie 2-e, dopolnennoe i pererabotannoe, Izd-vo Faktorial Press, Moskva, 2000
Bolsinov A.V., Fomenko A.T., Geometriya i topologiya integriruemykh geodezicheskikh potokov na poverkhnostyakh, v. 2, Biblioteka R&C Dynamics. Regulyarnaya i khaoticheskaya dinamika, URSS, Moskva, 1999
143.
Bolsinov A.V., Fomenko A.T., Integriruemye gamiltonovy sistemy. Geometriya. Topologiya. Klassifikatsiya, v. 1, 2, Izdatelskii dom “Udmurtskii universitet”, Izhevsk, 1999, 1: 444 c.; 2: 447 pp.
144.
Fomenko A.T., “Three-dimensional visualization of multidimensional topological objects”, International Journal of Shape Modeling, 5:1 (1999), 39–54
Fomenko A.T., Metody statisticheskogo analiza istoricheskikh tekstov. Prilozheniya k khronologii, v. 1, 2, Izd-vo Kraft+Lean, Moskva, 1999
146.
Kellin N.S., Nosovskii G.V., Fomenko A.T., “Vopros o podlinnosti “Drevnei Rosskiiskoi istorii” M. V. Lomonosova. Lomonosov ili Miller?”, Vestnik Moskovskogo Universiteta. Seriya 9: Filologiya, 1999, no. 1, 116–125
147.
Fomenko A.T., Differentsialnaya geometriya i topologiya. Dopolnitelnye glavy, v. 3, Biblioteka “Matematika”, izdanie 2-e, ispravlennoe i dopolnennoe, Regulyarnaya i khaoticheskaya dinamika, Izhevsk, 1999
V. V. Aleksandrov, V. S. Vladimirov, A. A. Gonchar, A. I. Grigor'ev, S. S. Grigoryan, S. V. Emel'yanov, V. A. Il'in, S. K. Korovin, D. P. Kostomarov, L. D. Kudryavtsev, L. S. Logunov, O. B. Lupanov, V. P. Maslov, E. I. Moiseev, O. A. Oleinik, Yu. S. Osipov, A. A. Samarskii, P. L. Ul'yanov, L. D. Faddeev, A. T. Fomenko, “Viktor Antonovich Sadovnichiǐ (on the occasion of his sixtieth birthday)”, Differ. Equ., 35:4 (1999), 433–446
1998
150.
Bolsinov A.V., Fomenko A.T., “Orbital isomorphism between two classical integrable systems. The Euler case and the Jacobi problem”, Lie groups and Lie algebras, Math. Appl., 433, Kluwer Acad. Publ., Dordrecht, 1998, 359–382
151.
A. V. Bolsinov, V. S. Matveev, A. T. Fomenko, “Two-dimensional Riemannian metrics with integrable geodesic flows. Local and global geometry”, Sb. Math., 189:10 (1998), 1441–1466
152.
Bolsinov A.V., Fomenko A.T., “Nekotorye aktualnye nereshennye zadachi po topologii integriruemykh gamiltonovykh sistem”, Topologicheskie metody v teorii gamiltonovykh sistem, izd-vo Faktorial, Moskva, 1998, 5–23
153.
Bolsinov A.V., Fomenko A.T., Matveev V.S., Riemannian metrics with integrable geodesic flows on surfaces: local and global geometry, Preprint series (120), Max-Planck-Institut für Mathematik, 1998, 42 pp.
154.
Matveev S.V., Fomenko A.T., Algoritmicheskie i kompyuternye metody v trekhmernoi topologii, vtoroe izdanie, pererabotannoe i dopolnennoe, Izd-vo Nauka, M., 1998
155.
Fomenko A.T., Naglyadnaya geometriya i topologiya. Matematicheskie obrazy v realnom mire, vtoroe izdanie, pererabotannoe i dopolnennoe, Izd-vo MGU, M., 1998
156.
G. I. Arkhipov, V. I. Blagodatskikh, A. A. Bolibrukh, V. A. Iskovskikh, A. A. Karatsuba, Yu. V. Prokhorov, A. T. Fomenko, V. N. Chubarikov, I. R. Shafarevich, “Sergei Mikhailovich Voronin (obituary)”, Russian Math. Surveys, 53:4 (1998), 777–781
1997
157.
A. V. Bolsinov, A. T. Fomenko, “On the dimension of the space of integrable Hamiltonian systems with two degrees of freedom”, Proc. Steklov Inst. Math., 216 (1997), 38–62
158.
Fomenko A.T., Matveev S.V., Algorithmic and computer methods for three-manifolds, Mathematics and its Applications, 425, Kluwer Academic Publishers, Dordrecht, 1997, xii+334 pp.
159.
Fomenko A.T., Kunii T.L., Topological modeling for visualization, Springer-Verlag, Tokyo, 1997, x+395 pp.
160.
Bolsinov A.V., Fomenko A.T., Vvedenie v topologiyu integriruemykh gamiltonovykh sistem, Nauka, M., 1997, 352 pp.
1999
161.
J. Math. Sci. (New York), 94:4 (1999), 1512–1557
162.
J. Math. Sci. (New York), 94:4 (1999), 1457–1476
1996
163.
Bolsinov A.V., Fomenko A.T., “Application of classification theory for integrable Hamiltonian systems to geodesic flows on $2$-sphere and $2$-torus and to the description of the topological structure of momentum mapping near singular points”, Dynamical systems, 1, J. Math. Sci., 78:5 (1996), 542–555
Fomenko A.T., Metody matematicheskogo analiza istoricheskikh tekstov. Prilozheniya k khronologii, Nauka, M., 1996, 478 pp. ; Fomenko A.T., Statistichka Khronologija. Matematichki pogled na istoriju. U kom smo veku?, Beograd, Yugoslaviya, 1997
165.
Nosovskii G.V., Fomenko A.T., “Matematiko-statisticheskie modeli raspredeleniya informatsii v istoricheskikh khronikakh”, Matematicheskie voprosy kibernetiki, 6, Nauka, fizmatlit, M., 1996, 71–116
1995
166.
Fomenko A.T., Symplectic geometry, Advanced Studies in Contemporary Mathematics, 5, Ed. 2, Gordon and Breach Publishers, Luxembourg, 1995, xvi+467 pp.
167.
Bolsinov A.V., Fomenko A.T., Zhang Xingru, “The strong, semi-strong, and quasi-semi-strong bordism groups of integrable Hamiltonian systems of differential equations with two degrees of freedom”, Russian J. Math. Phys., 3:4 (1995), 423–452
168.
A. V. Bolsinov, A. T. Fomenko, “Orbital Classification of Geodesic Flows on Two-Dimensional Ellipsoids. The Jacobi Problem is Orbitally Equivalent to the Integrable Euler Case in Rigid Body Dynamics”, Funct. Anal. Appl., 29:3 (1995), 149–160
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