Persons: Fomenko Anatoly Timofeevich

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Fomenko Anatoly Timofeevich

Statistics Math-Net.Ru
Total publications:	57
Scientific articles:	47
Citations to the author:	463
Cited articles:	39
Citing authors:	107

Number of views:
This page:	1554
Abstract pages:	5554
Full texts:	1561
References:	311

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:

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

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. Fomenko Mat. 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. Fomenko Tr. Geom. Semin., 2003, 24, 107–120
3.	Riemannian geometry V. V. Trofimov, A. T. Fomenko Itogi 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. Fomenko Mat. 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. Fomenko Mat. 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. Fomenko Tr. Mat. Inst. Steklova, 1997, 216, 45–69
7.	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. Fomenko Funkts. Anal. Prilozh., 1995, 29:3, 1–15
8.	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. Fomenko Izv. RAN. Ser. Mat., 1995, 59:1, 65–102
9.	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. Fomenko UMN, 1995, 50:3(303), 3–32
10.	A criterion for the topological conjugacy of Hamiltonian flows on two-dimensional compact surfaces A. V. Bolsinov, A. T. Fomenko UMN, 1995, 50:1(301), 189–190
11.	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. Fomenko Mat. Zametki, 1994, 56:2, 139–142
12.	Orbital equivalence of integrable Hamiltonian systems with two degrees of freedom. A classification theorem. II A. V. Bolsinov, A. T. Fomenko Mat. Sb., 1994, 185:5, 27–78
13.	Orbital equivalence of integrable Hamiltonian systems with two degrees of freedom. A classification theorem. I A. V. Bolsinov, A. T. Fomenko Mat. Sb., 1994, 185:4, 27–80
14.	Three types bordisms of integrable systems with two degrees of freedom. Computation of bordism groups A. V. Bolsinov, A. T. Fomenko, X. Zhang Trudy Mat. Inst. Steklov., 1994, 205, 32–72
15.	Unsolved problems in the theory of topological classification of integrable systems A. V. Bolsinov, A. T. Fomenko Trudy Mat. Inst. Steklov., 1994, 205, 18–31
16.	Trajectory classification of integrable systems of Euler type in the dynamics of a rigid body A. V. Bolsinov, A. T. Fomenko UMN, 1993, 48:5(293), 163–164
17.	A topological invariant which roughly classifies integrable strictly nondegenerate Hamiltonians on four-dimensional symplectic manifolds A. T. Fomenko Funkts. Anal. Prilozh., 1991, 25:4, 23–35
18.	A bordism theory for integrable nondegenerate Hamiltonian systems with two degrees of freedom. A new topological invariant of higher-dimensional integrable systems A. T. Fomenko Izv. Akad. Nauk SSSR Ser. Mat., 1991, 55:4, 747–779
19.	Recursion relations for homogeneous terms of a convergent series of the logarithm of a multiplicative integral on Lie groups A. T. Fomenko, R. V. Chakon Funkts. Anal. Prilozh., 1990, 24:1, 48–58
20.	A topological invariant and a criterion for the equivalence of integrable Hamiltonian systems with two degrees of freedom A. T. Fomenko, H. Zieschang Izv. Akad. Nauk SSSR Ser. Mat., 1990, 54:3, 546–575
21.	Topological classification of integrable non-degenerate Hamiltonians on a constant energy three-dimensional sphere Nguyen Tien Zung, A. T. Fomenko UMN, 1990, 45:6(276), 91–111
22.	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. Fomenko UMN, 1990, 45:2(272), 49–77
23.	The symplectic topology of completely integrable Hamiltonian systems A. T. Fomenko UMN, 1989, 44:1(265), 145–173
24.	Topological invariants of Liouville integrable Hamiltonian systems A. T. Fomenko Funkts. Anal. Prilozh., 1988, 22:4, 38–51
25.	On typical topological properties of integrable Hamiltonian systems A. T. Fomenko, H. Zieschang Izv. Akad. Nauk SSSR Ser. Mat., 1988, 52:2, 378–407
26.	Morse-type theory for integrable Hamiltonian systems with tame integrals S. V. Matveev, A. T. Fomenko Mat. Zametki, 1988, 43:5, 663–671
27.	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. Fomenko UMN, 1988, 43:1(259), 5–22
28.	Round Morse functions and isoenergy surfaces of integrable Hamiltonian systems S. V. Matveev, A. T. Fomenko, V. V. Sharko Mat. Sb. (N.S.), 1988, 135(177):3, 325–345
29.	Geometric and algebraic mechanisms for the integrability of Hamiltonian systems on homogeneous spaces and Lie algebras V. V. Trofimov, A. T. Fomenko Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 1987, 16, 227–299
30.	Test for minimality of lagrangian submanifolds in Kдhlerian ones Lê Hông Vân, A. T. Fomenko Mat. Zametki, 1987, 42:4, 559–571
31.	The topology of integral submanifolds of completely integrable Hamiltonian systems A. V. Brailov, A. T. Fomenko Mat. Sb. (N.S.), 1987, 134(176):3(11), 375–385
32.	The topology of surfaces of constant energy in integrable Hamiltonian systems, and obstructions to integrability A. T. Fomenko Izv. Akad. Nauk SSSR Ser. Mat., 1986, 50:6, 1276–1307
33.	The geometry of Poisson brackets and methods for integration, in the sense of Liouville, of systems on symmetric spaces V. V. Trofimov, A. T. Fomenko Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 1986, 29, 3–108
34.	Liouville integrability of Hamiltonian systems on Lie algebras V. V. Trofimov, A. T. Fomenko UMN, 1984, 39:2(236), 3–56
35.	Dynamical systems on the orbits of linear representations of Lie groups and the complete integrability of certain hydrodynamical systems V. V. Trofimov, A. T. Fomenko Funkts. Anal. Prilozh., 1983, 17:1, 31–39
36.	On minimal volumes of topological globally minimal surfaces in cobordisms A. T. Fomenko Izv. Akad. Nauk SSSR Ser. Mat., 1981, 45:1, 187–213
37.	Multi-dimensional variational methods in the topology of extremals A. T. Fomenko UMN, 1981, 36:6(222), 105–135
38.	On symplectic structures and integrable systems on symmetric spaces A. T. Fomenko Mat. Sb. (N.S.), 1981, 115(157):2(6), 263–280
39.	The index of elliptic operators over $C^$-algebras A. S. Mishchenko, A. T. Fomenko Izv. Akad. Nauk SSSR Ser. Mat.*, 1979, 43:4, 831–859
40.	Generalized Liouville method of integration of Hamiltonian systems A. S. Mishchenko, A. T. Fomenko Funkts. Anal. Prilozh., 1978, 12:2, 46–56
41.	Euler equations on finite-dimensional Lie groups A. S. Mishchenko, A. T. Fomenko Izv. Akad. Nauk SSSR Ser. Mat., 1978, 42:2, 396–415
42.	The problem of discriminating algorithmically the standard three-dimensional sphere I. A. Volodin, V. E. Kuznetsov, A. T. Fomenko UMN, 1974, 29:5(179), 71–168
43.	Geometric variational problems A. T. Fomenko Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat., 1973, 1, 39–60
44.	The multidimensional plateau problem in Riemannian varieties A. T. Fomenko Mat. Zametki, 1973, 13:1, 159–167
45.	Minimal compacta in riemannian manifolds and Reifenberg's conjecture A. T. Fomenko Izv. Akad. Nauk SSSR Ser. Mat., 1972, 36:5, 1049–1079
46.	The multidimensional Plateau problem in Riemannian manifolds A. T. Fomenko Mat. Sb. (N.S.), 1972, 89(131):3(11), 475–519
47.	Bott periodicity from the point of view of an $n$-dimensional Dirichlet functional A. T. Fomenko Izv. Akad. Nauk SSSR Ser. Mat., 1971, 35:3, 667–681

48.	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. Chernavskii UMN, 2008, 63:4(382), 173–174
49.	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. Shavgulidze UMN, 2004, 59:5(359), 135–140
50.	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. Fomenko UMN, 2001, 56:1(337), 201–204
51.	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. Shafarevich UMN, 1998, 53:4(322), 125–128
52.	Ol'ga Arsen'evna Oleinik (on her seventieth birthday) N. S. Bakhvalov, S. P. Novikov, A. T. Fomenko UMN, 1995, 50:4(304), 177–186
53.	Preface A. T. Fomenko Trudy Mat. Inst. Steklov., 1994, 205, 3
54.	Aleksandr Petrovich Norden (obituary) V. V. Vishnevskii, B. N. Shapukov, A. P. Shirokov, M. A. Akivis, A. T. Fomenko, S. P. Novikov, Ya. G. Sinai UMN, 1993, 48:4(292), 169–170
55.	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. Ryzhkov UMN, 1993, 48:3(291), 213–216
56.	Petr Konstantinovich Rashevskii (on his seventieth birthday) S. P. Novikov, A. T. Fomenko UMN, 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

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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