Fomenko Anatoly Timofeevich
Statistics Math-Net.Ru
Total publications:
59
Scientific articles:
49
Citations to the author:
488
Cited articles:
39
Citing authors:
117
Number of views:
This page: 1831 Abstract pages: 6728 Full texts: 1971 References: 329
Academic status:
Member of the Russian Academy of Sciences
Scientific status:
Professor
Scientific degree:
Doctor of physico-mathematical sciences (1973)
Speciality:
01.01.04 (Geometry and topology)
Birth date:
13.03.1945
Phone:
+7 (495) 939 39 40
Fax:
+7 (495) 932 89 94
E-mail:
fomenko®mech.math.msu¸su , fom®difgeo.math.msu¸su
Keywords:
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.
UDC:
513.8, 513.83, 513.834, 513.836, 513.944, 514 , 515.1 , 515.162.3 , 515.164.174 , 515.164.8 , 516.96, 517.9, 517.925.53 , 517.938.5 , 517.97 , 519.177.3 , 519.3, 519.46, 519.944, 517.946
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
Fomenko A. T., “Simplekticheskaya topologiya vpolne integriruemykh gamiltonovykh sistem”, UMN , 44 :1 (1989), 145–173
List of publications on Google Scholar
List of publications on ZentralBlatt
Personal webpage on MathSciNet
Publications in Math-Net.Ru
1.
Maximally symmetric cell decompositions of surfaces
and their coverings E. A. Kudryavtseva, I. M. Nikonov, A. T. FomenkoMat. Sb. , 2008 , 199 :9, 3–96
2.
New results on topological classification
of integrable systems in the mechanics of rigid body P. V. Morozov, A. T. FomenkoTr. Geom. Semin. , 2003 , 24 , 107–120
3.
Riemannian geometry V. V. Trofimov, A. T. FomenkoItogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz. , 2002 , 76 , 5–262
4.
The method of loop molecules and the topology of the Kovalevskaya top A. V. Bolsinov, P. H. Richter, A. T. FomenkoMat. Sb. , 2000 , 191 :2, 3–42
5.
Two-dimensional Riemannian metrics with integrable geodesic flows. Local and global geometry A. V. Bolsinov, V. S. Matveev, A. T. FomenkoMat. Sb. , 1998 , 189 :10, 5–32
6.
On the dimension of the space of integrable Hamiltonian systems with two degrees of freedom A. V. Bolsinov, A. T. FomenkoTr. Mat. Inst. Steklova , 1997 , 216 , 45–69
7.
Symplectic topology of integrable dynamical systems. Rough topological classification of classical cases of integrability in the dynamics of a heavy rigid body A. T. FomenkoZap. Nauchn. Sem. POMI , 1996 , 235 , 104–183
8.
Exact topological classification of Hamiltonian flows on smooth two-dimensional surfaces A. V. Bolsinov, A. T. FomenkoZap. Nauchn. Sem. POMI , 1996 , 235 , 22–53
9.
Orbital Classification of Geodesic Flows on Two-Dimensional Ellipsoids. The Jacobi Problem is Orbitally Equivalent
to the Integrable Euler Case in Rigid Body Dynamics A. V. Bolsinov, A. T. FomenkoFunkts. Anal. Prilozh. , 1995 , 29 :3, 1–15
10.
Orbital invariants of integrable Hamiltonian systems. The case of simple systems. Orbital classification of systems of Euler type in rigid body dynamics A. V. Bolsinov, A. T. FomenkoIzv. RAN. Ser. Mat. , 1995 , 59 :1, 65–102
11.
The Maupertuis principle and geodesic flows on the sphere arising from integrable cases in the dynamics of a rigid body A. V. Bolsinov, V. V. Kozlov, A. T. FomenkoUspekhi Mat. Nauk , 1995 , 50 :3(303), 3–32
12.
A criterion for the topological conjugacy of Hamiltonian flows on two-dimensional compact surfaces A. V. Bolsinov, A. T. FomenkoUspekhi Mat. Nauk , 1995 , 50 :1(301), 189–190
13.
Integrable geodesic flows on the sphere, generated by Goryachev–Chaplygin and Kowalewski systems in the dynamics of a rigid body A. V. Bolsinov, A. T. FomenkoMat. Zametki , 1994 , 56 :2, 139–142
14.
Orbital equivalence of integrable Hamiltonian systems with two degrees of freedom. A classification theorem. II A. V. Bolsinov, A. T. FomenkoMat. Sb. , 1994 , 185 :5, 27–78
15.
Orbital equivalence of integrable Hamiltonian systems with two degrees of freedom. A classification theorem. I A. V. Bolsinov, A. T. FomenkoMat. Sb. , 1994 , 185 :4, 27–80
16.
Three types bordisms of integrable systems with two degrees of freedom. Computation of bordism groups A. V. Bolsinov, A. T. Fomenko, X. ZhangTrudy Mat. Inst. Steklov. , 1994 , 205 , 32–72
17.
Unsolved problems in the theory of topological classification of integrable systems A. V. Bolsinov, A. T. FomenkoTrudy Mat. Inst. Steklov. , 1994 , 205 , 18–31
18.
Trajectory classification of integrable systems of Euler type in the dynamics of a rigid body A. V. Bolsinov, A. T. FomenkoUspekhi Mat. Nauk , 1993 , 48 :5(293), 163–164
19.
A topological invariant which roughly classifies integrable strictly nondegenerate Hamiltonians on four-dimensional symplectic manifolds A. T. FomenkoFunkts. Anal. Prilozh. , 1991 , 25 :4, 23–35
20.
A bordism theory for integrable nondegenerate Hamiltonian systems with two degrees of freedom. A new topological invariant of higher-dimensional integrable systems A. T. FomenkoIzv. Akad. Nauk SSSR Ser. Mat. , 1991 , 55 :4, 747–779
21.
Recursion relations for homogeneous terms of a convergent series of the logarithm of a multiplicative integral on Lie groups A. T. Fomenko, R. V. ChakonFunkts. Anal. Prilozh. , 1990 , 24 :1, 48–58
22.
A topological invariant and a criterion for the equivalence of integrable Hamiltonian systems with two degrees of freedom A. T. Fomenko, H. ZieschangIzv. Akad. Nauk SSSR Ser. Mat. , 1990 , 54 :3, 546–575
23.
Topological classification of integrable non-degenerate Hamiltonians on a constant energy three-dimensional sphere Nguyen Tien Zung, A. T. FomenkoUspekhi Mat. Nauk , 1990 , 45 :6(276), 91–111
24.
Topological classification of integrable Hamiltonian systems with two degrees of freedom. List of systems of small complexity A. V. Bolsinov, S. V. Matveev, A. T. FomenkoUspekhi Mat. Nauk , 1990 , 45 :2(272), 49–77
25.
The symplectic topology of completely integrable Hamiltonian systems A. T. FomenkoUspekhi Mat. Nauk , 1989 , 44 :1(265), 145–173
26.
Topological invariants of Liouville integrable Hamiltonian systems A. T. FomenkoFunkts. Anal. Prilozh. , 1988 , 22 :4, 38–51
27.
On typical topological properties of integrable Hamiltonian systems A. T. Fomenko, H. ZieschangIzv. Akad. Nauk SSSR Ser. Mat. , 1988 , 52 :2, 378–407
28.
Morse-type theory for integrable Hamiltonian systems with tame integrals S. V. Matveev, A. T. FomenkoMat. Zametki , 1988 , 43 :5, 663–671
29.
Constant energy surfaces of Hamiltonian systems, enumeration of three-dimensional manifolds in increasing order of complexity, and computation of volumes of closed hyperbolic manifolds S. V. Matveev, A. T. FomenkoUspekhi Mat. Nauk , 1988 , 43 :1(259), 5–22
30.
Round Morse functions and isoenergy surfaces of integrable Hamiltonian systems S. V. Matveev, A. T. Fomenko, V. V. SharkoMat. Sb. (N.S.) , 1988 , 135(177) :3, 325–345
31.
Geometric and algebraic mechanisms for the integrability of Hamiltonian systems on homogeneous spaces and Lie algebras V. V. Trofimov, A. T. FomenkoItogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr. , 1987 , 16 , 227–299
32.
Test for minimality of lagrangian submanifolds in Kдhlerian ones Lê Hông Vân, A. T. FomenkoMat. Zametki , 1987 , 42 :4, 559–571
33.
The topology of integral submanifolds of completely integrable Hamiltonian systems A. V. Brailov, A. T. FomenkoMat. Sb. (N.S.) , 1987 , 134(176) :3(11), 375–385
34.
The topology of surfaces of constant energy in integrable Hamiltonian systems, and obstructions to integrability A. T. FomenkoIzv. Akad. Nauk SSSR Ser. Mat. , 1986 , 50 :6, 1276–1307
35.
The geometry of Poisson brackets and methods for integration, in the sense of Liouville, of systems on symmetric spaces V. V. Trofimov, A. T. FomenkoItogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh. , 1986 , 29 , 3–108
36.
Liouville integrability of Hamiltonian systems on Lie algebras V. V. Trofimov, A. T. FomenkoUspekhi Mat. Nauk , 1984 , 39 :2(236), 3–56
37.
Dynamical systems on the orbits of linear representations of Lie groups and the complete integrability of certain hydrodynamical systems V. V. Trofimov, A. T. FomenkoFunkts. Anal. Prilozh. , 1983 , 17 :1, 31–39
38.
On minimal volumes of topological globally minimal surfaces in cobordisms A. T. FomenkoIzv. Akad. Nauk SSSR Ser. Mat. , 1981 , 45 :1, 187–213
39.
Multi-dimensional variational methods in the topology of extremals A. T. FomenkoUspekhi Mat. Nauk , 1981 , 36 :6(222), 105–135
40.
On symplectic structures and integrable systems on symmetric spaces A. T. FomenkoMat. Sb. (N.S.) , 1981 , 115(157) :2(6), 263–280
41.
The index of elliptic operators over $C^*$ -algebras A. S. Mishchenko, A. T. FomenkoIzv. Akad. Nauk SSSR Ser. Mat. , 1979 , 43 :4, 831–859
42.
Generalized Liouville method of integration of Hamiltonian systems A. S. Mishchenko, A. T. FomenkoFunkts. Anal. Prilozh. , 1978 , 12 :2, 46–56
43.
Euler equations on finite-dimensional Lie groups A. S. Mishchenko, A. T. FomenkoIzv. Akad. Nauk SSSR Ser. Mat. , 1978 , 42 :2, 396–415
44.
The problem of discriminating algorithmically the standard three-dimensional sphere I. A. Volodin, V. E. Kuznetsov, A. T. FomenkoUspekhi Mat. Nauk , 1974 , 29 :5(179), 71–168
45.
Geometric variational problems A. T. FomenkoItogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. , 1973 , 1 , 39–60
46.
The multidimensional plateau problem in Riemannian varieties A. T. FomenkoMat. Zametki , 1973 , 13 :1, 159–167
47.
Minimal compacta in riemannian manifolds and Reifenberg's conjecture A. T. FomenkoIzv. Akad. Nauk SSSR Ser. Mat. , 1972 , 36 :5, 1049–1079
48.
The multidimensional Plateau problem in Riemannian manifolds A. T. FomenkoMat. Sb. (N.S.) , 1972 , 89(131) :3(11), 475–519
49.
Bott periodicity from the point of view of an $n$ -dimensional Dirichlet functional A. T. FomenkoIzv. Akad. Nauk SSSR Ser. Mat. , 1971 , 35 :3, 667–681
50.
Yurii Grigor'evich Borisovich (obituary) 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. ChernavskiiUspekhi Mat. Nauk , 2008 , 63 :4(382), 173–174
51.
Yurii Petrovich Solov'ev (obituary) V. V. Belokurov, A. A. Egorov, A. S. Mishchenko, F. Yu. Popelenskii, V. A. Sadovnichii, E. V. Troitskii, A. T. Fomenko, E. T. ShavgulidzeUspekhi Mat. Nauk , 2004 , 59 :5(359), 135–140
52.
Anatolii Mikhailovich Stepin (on his 60th birthday)
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. FomenkoUspekhi Mat. Nauk , 2001 , 56 :1(337), 201–204
53.
Sergei Mikhailovich Voronin (obituary) 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. ShafarevichUspekhi Mat. Nauk , 1998 , 53 :4(322), 125–128
54.
Ol'ga Arsen'evna Oleinik (on her seventieth birthday) N. S. Bakhvalov, S. P. Novikov, A. T. FomenkoUspekhi Mat. Nauk , 1995 , 50 :4(304), 177–186
55.
Preface A. T. FomenkoTrudy Mat. Inst. Steklov. , 1994 , 205 , 3
56.
Aleksandr Petrovich Norden (obituary) V. V. Vishnevskii, B. N. Shapukov, A. P. Shirokov, M. A. Akivis, A. T. Fomenko, S. P. Novikov, Ya. G. SinaiUspekhi Mat. Nauk , 1993 , 48 :4(292), 169–170
57.
Maks Aizikovich Akivis (on the occasion of his 70th birthday and 50 years of scientific activity) V. V. Goldberg, A. M. Shelekhov, A. T. Fomenko, V. F. Kirichenko, V. V. RyzhkovUspekhi Mat. Nauk , 1993 , 48 :3(291), 213–216
58.
Petr Konstantinovich Rashevskii (on his seventieth birthday) S. P. Novikov, A. T. FomenkoUspekhi Mat. Nauk , 1977 , 32 :5(197), 205–209
Книги в базе данных Math-Net.Ru
New results in the theory of topological classification of integrable systems , Trudy Mat. Inst. Steklov., 205 , ed. A. T. Fomenko, E. F. Mishchenko, 1994, 208 с.http://mi.mathnet.ru/book1092
Organisations