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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: ,
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
  1. Fomenko A. T., “Periodichnost Botta s tochki zreniya mnogomernogo funktsionala Dirikhle”, Izv. AN SSSR. Ser. matem., 35:3 (1971), 667–681  mathnet  mathscinet  zmath
  2. Fomenko A. T., “Mnogomernaya zadacha Plato v rimanovykh mnogoobraziyakh”, Matem. sb., 89:3 (1972), 475–519  mathnet  mathscinet  zmath
  3. Mischenko A. S., Fomenko A. T., “Obobschennyi metod Liuvillya integrirovaniya gamiltonovykh sistem”, Funkts. analiz i ego prilozh., 12:2 (1978), 46–56  mathnet  mathscinet  zmath
  4. Fomenko A. T., “Teoriya Morsa integriruemykh gamiltonovykh sistem”, Dokl. AN SSSR, 287:5 (1986), 1071–1075  mathscinet  zmath
  5. Fomenko A. T., “Simplekticheskaya topologiya vpolne integriruemykh gamiltonovykh sistem”, UMN, 44:1 (1989), 145–173  mathnet  mathscinet  zmath

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. Symplectic topology of integrable dynamical systems. Rough topological classification of classical cases of integrability in the dynamics of a heavy rigid body
A. T. Fomenko
Zap. Nauchn. Sem. POMI, 1996, 235, 104–183
8. Exact topological classification of Hamiltonian flows on smooth two-dimensional surfaces
A. V. Bolsinov, A. T. Fomenko
Zap. 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. Fomenko
Funkts. 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. Fomenko
Izv. 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. Fomenko
Uspekhi 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. Fomenko
Uspekhi 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. Fomenko
Mat. 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. Fomenko
Mat. 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. Fomenko
Mat. 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. Zhang
Trudy Mat. Inst. Steklov., 1994, 205, 32–72
17. 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
18. Trajectory classification of integrable systems of Euler type in the dynamics of a rigid body
A. V. Bolsinov, A. T. Fomenko
Uspekhi 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. Fomenko
Funkts. 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. Fomenko
Izv. 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. Chakon
Funkts. 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. Zieschang
Izv. 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. Fomenko
Uspekhi 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. Fomenko
Uspekhi Mat. Nauk, 1990, 45:2(272), 49–77
25. The symplectic topology of completely integrable Hamiltonian systems
A. T. Fomenko
Uspekhi Mat. Nauk, 1989, 44:1(265), 145–173
26. Topological invariants of Liouville integrable Hamiltonian systems
A. T. Fomenko
Funkts. Anal. Prilozh., 1988, 22:4, 38–51
27. On typical topological properties of integrable Hamiltonian systems
A. T. Fomenko, H. Zieschang
Izv. 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. Fomenko
Mat. 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. Fomenko
Uspekhi 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. Sharko
Mat. 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. Fomenko
Itogi 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. Fomenko
Mat. Zametki, 1987, 42:4, 559–571
33. 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
34. 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
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. Fomenko
Itogi 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. Fomenko
Uspekhi 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. Fomenko
Funkts. Anal. Prilozh., 1983, 17:1, 31–39
38. On minimal volumes of topological globally minimal surfaces in cobordisms
A. T. Fomenko
Izv. Akad. Nauk SSSR Ser. Mat., 1981, 45:1, 187–213
39. Multi-dimensional variational methods in the topology of extremals
A. T. Fomenko
Uspekhi Mat. Nauk, 1981, 36:6(222), 105–135
40. On symplectic structures and integrable systems on symmetric spaces
A. T. Fomenko
Mat. Sb. (N.S.), 1981, 115(157):2(6), 263–280
41. 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
42. Generalized Liouville method of integration of Hamiltonian systems
A. S. Mishchenko, A. T. Fomenko
Funkts. Anal. Prilozh., 1978, 12:2, 46–56
43. Euler equations on finite-dimensional Lie groups
A. S. Mishchenko, A. T. Fomenko
Izv. 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. Fomenko
Uspekhi Mat. Nauk, 1974, 29:5(179), 71–168
45. Geometric variational problems
A. T. Fomenko
Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat., 1973, 1, 39–60
46. The multidimensional plateau problem in Riemannian varieties
A. T. Fomenko
Mat. Zametki, 1973, 13:1, 159–167
47. Minimal compacta in riemannian manifolds and Reifenberg's conjecture
A. T. Fomenko
Izv. Akad. Nauk SSSR Ser. Mat., 1972, 36:5, 1049–1079
48. The multidimensional Plateau problem in Riemannian manifolds
A. T. Fomenko
Mat. 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. Fomenko
Izv. 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. Chernavskii
Uspekhi 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. Shavgulidze
Uspekhi 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. Fomenko
Uspekhi 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. Shafarevich
Uspekhi 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. Fomenko
Uspekhi Mat. Nauk, 1995, 50:4(304), 177–186
55. Preface
A. T. Fomenko
Trudy 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. Sinai
Uspekhi 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. Ryzhkov
Uspekhi Mat. Nauk, 1993, 48:3(291), 213–216
58. Petr Konstantinovich Rashevskii (on his seventieth birthday)
S. P. Novikov, A. T. Fomenko
Uspekhi Mat. Nauk, 1977, 32:5(197), 205–209

Книги в базе данных Math-Net.Ru
  1. 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

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