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## Fomenko, Anatoliĭ Timofeevich

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 Author ID: fomenko.anatoly-t Published as: Fomenko, A.; Fomenko, A. T.; Fomenko, Anatolii T.; Fomenko, Anatolij T.; Fomenko, Anatoliĭ T.; Fomenko, Anatoly; Fomenko, Anatoly T. Homepage: http://www.anatoly-fomenko.com/ External Links: MGP · Math-Net.Ru · Wikidata · GND
 Documents Indexed: 258 Publications since 1969, including 62 Books Biographic References: 3 Publications
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#### Serials

 19 Russian Mathematical Surveys 15 Soviet Mathematics. Doklady 15 Trudy Seminara po Vektornomu i Tenzornomu Analizu 9 Mathematics of the USSR. Izvestiya 8 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 7 Journal of Mathematical Sciences (New York) 6 Functional Analysis and its Applications 5 Journal of Soviet Mathematics 5 Doklady Mathematics 5 Graduate Texts in Mathematics 4 Moscow University Mathematics Bulletin 4 Uspekhi Matematicheskikh Nauk [N. S.] 4 Mathematics of the USSR, Sbornik 4 Vestnik Moskovskogo Universiteta. Seriya I. Matematika, Mekhanika 3 Mathematical Notes 3 Selecta Mathematica Sovietica 3 Acta Applicandae Mathematicae 3 Russian Journal of Mathematical Physics 3 Sbornik: Mathematics 3 Izvestiya: Mathematics 2 Matematicheskie Zametki 2 Advances in Mathematics 2 Funktsional’nyĭ Analiz i ego Prilozheniya 2 Matematicheskiĭ Sbornik. Novaya Seriya 2 Russian Academy of Sciences. Sbornik. Mathematics 2 Russian Academy of Sciences. Doklady. Mathematics 2 Advances in Soviet Mathematics 2 Translations of Mathematical Monographs 2 Translations. Series 2. American Mathematical Society 1 Computers & Mathematics with Applications 1 Ukrainian Mathematical Journal 1 Journal of Geometry and Physics 1 International Statistical Review 1 Topology and its Applications 1 Comptes Rendus Mathématiques de l’Académie des Sciences 1 Annals of Global Analysis and Geometry 1 Matematicheskie Voprosy Kibernetiki 1 Trudy Geometricheskogo Seminara 1 Istoriko-Matematicheskie Issledovaniya. Vtoraya Seriya 1 International Journal of Shape Modeling 1 Reviews in Mathematics and Mathematical Physics 1 Issledovanie Operatsiĭ i ASU 1 Differential Equations 1 Theoretical and Applied Mechanics 1 Semiotika i Informatika 1 Journal of Generalized Lie Theory and Applications 1 Journal of Fixed Point Theory and Applications
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#### Fields

 124 Dynamical systems and ergodic theory (37-XX) 89 Differential geometry (53-XX) 61 Global analysis, analysis on manifolds (58-XX) 49 Manifolds and cell complexes (57-XX) 47 Mechanics of particles and systems (70-XX) 35 Calculus of variations and optimal control; optimization (49-XX) 30 History and biography (01-XX) 27 Algebraic topology (55-XX) 19 General and overarching topics; collections (00-XX) 15 Nonassociative rings and algebras (17-XX) 14 Topological groups, Lie groups (22-XX) 12 Statistics (62-XX) 8 Geometry (51-XX) 8 Computer science (68-XX) 7 General topology (54-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Partial differential equations (35-XX) 5 Astronomy and astrophysics (85-XX) 4 Fluid mechanics (76-XX) 4 Relativity and gravitational theory (83-XX) 3 Group theory and generalizations (20-XX) 3 Operator theory (47-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Ordinary differential equations (34-XX) 2 Functional analysis (46-XX) 2 Quantum theory (81-XX) 2 Biology and other natural sciences (92-XX) 1 Combinatorics (05-XX) 1 Number theory (11-XX) 1 Algebraic geometry (14-XX) 1 $$K$$-theory (19-XX) 1 Measure and integration (28-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Convex and discrete geometry (52-XX) 1 Numerical analysis (65-XX) 1 Mechanics of deformable solids (74-XX) 1 Mathematics education (97-XX)

#### Citations contained in zbMATH Open

166 Publications have been cited 2,009 times in 1,223 Documents Cited by Year
Integrable Hamiltonian systems. Geometry, topology, classification. Translated from the 1999 Russian original. Zbl 1056.37075
Bolsinov, A. V.; Fomenko, A. T.
2004
Modern geometry - methods and applications. Part I. The geometry of surfaces, transformation groups, and fields. Transl. by Robert G. Burns. 2nd ed. Zbl 0751.53001
Dubrovin, B. A.; Fomenko, A. T.; Novikov, S. P.
1992
Modern geometry - methods and applications. Part I: The geometry of surfaces, transformation groups, and fields. Transl. from the Russian by Robert G. Burns. Zbl 0529.53002
Dubrovin, B. A.; Fomenko, A. T.; Novikov, S. P.
1984
Modern geometry - methods and applications. Part 2: The geometry and topology of manifolds. Transl. from the Russian by Robert G. Burns. Zbl 0565.57001
Dubrovin, B. A.; Fomenko, A. T.; Novikov, S. P.
1985
Euler equations on finite-dimensional Lie groups. Zbl 0383.58006
Mishchenko, A. S.; Fomenko, A. T.
1978
Integrable Hamiltonian systems. Geometry, topology, classification. Vol. 1, 2. Zbl 1053.37518
Bolsinov, A. V.; Fomenko, A. T.
1999
Generalized Liouville method of integration of Hamiltonian systems. Zbl 0405.58028
Mishchenko, A. S.; Fomenko, A. T.
1978
Modern geometry. Methods and applications. Textbook. (Sovremennaya geometriya. Metody i prilozheniya. Uchebnoe posobie). 2nd ed., rev. Zbl 0601.53001
Dubrovin, B. A.; Novikov, S. P.; Fomenko, A. T.
1986
The index of elliptic operators over $$C^*$$-algebras. Zbl 0416.46052
Mishchenko, A. S.; Fomenko, A. T.
1979
Algebra and geometry of integrable Hamiltonian differential equations. Zbl 0858.58026
Trofimov, V. V.; Fomenko, A. T.
1995
Integrability and nonintegrability in geometry and mechanics. Transl. from the Russian by M. V. Tsaplina. Zbl 0675.58018
Fomenko, A. T.
1988
Euler equations on finite-dimensional Lie groups. Zbl 0405.58031
Mishchenko, A. S.; Fomenko, A. T.
1978
A course in homotopic topology. Textbook. Zbl 0675.55001
Fomenko, A. T.; Fuks, D. B.
1989
Topological invariant and a criterion for equivalence of integrable Hamiltonian systems with two degrees of freedom. Zbl 0705.58023
Fomenko, A. T.; Zieschang, H.
1990
Modern geometry - methods and applications. Part III. Introduction to homology theory. Transl. from the Russian by Robert G. Burns. Zbl 0703.55001
Dubrovin, B. A.; Fomenko, A. T.; Novikov, S. P.
1990
The problem of discriminating algorithmically the standard three- dimensional sphere. Zbl 0311.57001
Volodin, I. A.; Kuznetsov, V. E.; Fomenko, A. T.
1974
Constant energy surfaces of Hamiltonian systems, enumeration of three- dimensional manifolds in increasing order of complexity, and computation of volumes of closed hyperbolic manifolds. Zbl 0671.58008
Matveev, S. V.; Fomenko, A. T.
1988
Topology of surfaces of constant energy of integrable Hamiltonian systems and barriers to integrability. Zbl 0619.58023
Fomenko, A. T.
1986
Maximally symmetric cell decompositions of surfaces and their coverings. Zbl 1163.37018
Kudryavtseva, E. A.; Nikonov, I. M.; Fomenko, A. T.
2008
Algorithmic and computer methods for three-manifolds. Transl. from the Russian by M. Tsaplina and M. Hazewinkel. Zbl 0885.57009
Fomenko, A. T.; Matveev, S. V.
1997
A course in differential geometry and topology. Textbook. (Kurs differentsial’noj geometrii i topologii. Uchebnik). Zbl 0524.53001
Mishchenko, A. S.; Fomenko, A. T.
1980
Modern geometry. (Sovremennaya geometriya). Zbl 0433.53001
Dubrovin, B. A.; Novikov, S. P.; Fomenko, A. T.
1980
Two-dimensional Riemannian metrics with integrable geodesic flows. Local and global geometry. Zbl 0917.58031
Bolsinov, A. V.; Matveev, V. S.; Fomenko, A. T.
1998
Introduction to the topology of integrable Hamiltonian systems. Zbl 0908.58026
Bolsinov, A. V.; Fomenko, A. T.
1997
Symplectic geometry. Methods and applications. Zbl 0751.53002
Fomenko, A. T.
1988
New approach to symmetries and singularities in integrable Hamiltonian systems. Zbl 1248.37050
Fomenko, A. T.; Konyaev, A. Yu.
2012
A topological invariant and a criterion for equivalence of integrable Hamiltonian systems with two degrees of freedom. Zbl 0723.58024
Fomenko, A. T.; Zieschang, H.
1991
Morse theory of integrable Hamiltonian systems. Zbl 0623.58009
Fomenko, A. T.
1986
The index of elliptic operators over $$C^*$$-algebras. Zbl 0448.46039
Mishchenko, A. S.; Fomenko, A. T.
1980
The Maupertuis principle and geodesic flows on the sphere arising from integrable cases in the dynamics of a rigid body. Zbl 0881.58031
Bolsinov, A. V.; Kozlov, V. V.; Fomenko, A. T.
1995
The symplectic topology of completely integrable Hamiltonian systems. Zbl 0694.58012
Fomenko, A. T.
1989
Topological invariants of Liouville integrable Hamiltonian systems. Zbl 0697.58021
Fomenko, A. T.
1988
Integrable billiards model important integrable cases of rigid body dynamics. Zbl 1335.37040
Fokicheva, V. V.; Fomenko, A. T.
2015
The method of loop molecules and the topology of the Kovalevskaya top. Zbl 0983.37068
Bolsinov, A. V.; Richter, P. H.; Fomenko, A. T.
2000
Topological classification of all integrable Hamiltonian differential equations of general type with two degrees of freedom. Zbl 0753.58014
Fomenko, A. T.
1991
Topological classification of integrable Hamiltonian systems with two degrees of freedom. List of systems of small complexity. Zbl 0705.58025
Bolsinov, A. V.; Matveev, S. V.; Fomenko, A. T.
1990
Symplectic topology of completely integrable Hamiltonian systems. Zbl 0677.58023
Fomenko, A. T.
1989
Algebra and geometry through Hamiltonian systems. Zbl 1362.70023
Fomenko, Anatoly T.; Konyaev, Andrei
2014
Symmetries groups of nice Morse functions on surfaces. Zbl 1295.58013
Kudryavtseva, E. A.; Fomenko, A. T.
2012
On typical topological properties of integrable Hamiltonian systems. Zbl 0647.58018
Fomenko, A. T.; Zieschang, H.
1988
Non-invariant symplectic group structures and Hamiltonian flows on symmetric spaces. Zbl 0659.58018
Trofimov, V. V.; Fomenko, A. T.
1988
The topology of surfaces of constant energy in integrable Hamiltonian systems, and obstructions to integrability. Zbl 0649.58019
Fomenko, A. T.
1987
Integrable topological billiards and equivalent dynamical systems. Zbl 1380.37078
Vedyushkina, Viktoriya V.; Fomenko, Anatoly T.
2017
Topological classification of integrable Hamiltonian systems with two degrees of freedom. List of systems of small complexity. Zbl 0696.58019
Bolsinov, A. V.; Matveev, S. V.; Fomenko, A. T.
1990
Integrable geodesic flows on two-dimensional surfaces. Zbl 1042.37042
Bolsinov, A. V.; Fomenko, A. T.
2000
Homotopic topology. (Transl. from the Russian by K. Mályusz). Zbl 0615.55001
Fomenko, A. T.; Fuks, D. B.; Gutenmacher, V. L.
1986
Differential geometry and topology. Complemented chapters. (Differentsial’naya geometriya i topologiya. Dopolnitel’nye glavy). Zbl 0517.53001
Fomenko, A. T.
1983
Symplectic geometry. 2nd ed. Zbl 0873.58031
Fomenko, A. T.
1995
The theory of invariants of multidimensional integrable Hamiltonian systems (with arbitrary many degrees of freedom). Molecular table of all integrable systems with two degrees of freedom. Zbl 0746.58036
Fomenko, A. T.
1991
Modern geometry. Methods of homology theory. Zbl 0582.55001
Dubrovin, B. A.; Novikov, S. P.; Fomenko, A. T.
1984
Liouville integrability of Hamiltonian systems on Lie algebras. Zbl 0549.58024
Trofimov, V. V.; Fomenko, A. T.
1984
Variational methods in topology. Zbl 0526.58012
Fomenko, A. T.
1982
The integrability of the Euler equations on semi-simple Lie algebras. Zbl 0452.58015
Mishchenko, A. S.; Fomenko, A. T.
1979
On the topology of the three-dimensional manifolds arising in Hamiltonian mechanics. Zbl 0734.57014
Fomenko, A. T.; Zieschang, H.
1987
A generalized Liouville method for the integration of Hamiltonian systems. Zbl 0396.58003
Mishchenko, A. S.; Fomenko, A. T.
1978
On typical topological properties of integrable Hamiltonian systems. Zbl 0667.58014
Fomenko, A. T.; Zieschang, H.
1989
Orbital classification of geodesic flows on two-dimensional ellipsoids. The Jacobi problem is orbitally equivalent to the integrable Euler case in rigid body dynamics. Zbl 0878.58036
Bolsinov, A. V.; Fomenko, A. T.
1995
Differential geometry and topology. Transl. from Russian by D. A. Leites. Zbl 0643.53003
Fomenko, A. T.
1987
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. Zbl 1358.37097
Fomenko, A. T.; Nikolaenko, S. S.
2015
Topological modeling for visualization. Zbl 1120.37300
Fomenko, A. T.; Kunii, T. L.
1997
Orbital equivalence of integrable Hamiltonian systems with two degrees of freedom. A classification theorem. I. Zbl 0828.58020
Bolsinov, A. V.; Fomenko, A. T.
1994
Elements of the geometry and topology of minimal surfaces in three-dimensional space. Transl. from the Russian by E. J. F. Primrose. Transl. ed. by Simeon Ivanov. Zbl 0745.53001
Fomenko, A. T.; Tuzhilin, A. A.
1991
On the integration of the Euler equations on semisimple Lie algebras. Zbl 0392.58001
Mishchenko, A. S.; Fomenko, A. T.
1976
Modeling nondegenerate bifurcations of closures of solutions for integrable systems with two degrees of freedom by integrable topological billiards. Zbl 1394.37088
Vedyushkina, V. V.; Fomenko, A. T.; Kharcheva, Irina S.
2018
Billiard systems as the models for the rigid body dynamics. Zbl 1362.70005
Fokicheva, Victoria V.; Fomenko, Anatoly T.
2016
Geometric and algebraic mechanisms of the integrability of Hamiltonian systems on homogeneous spaces and Lie algebras. Zbl 0797.58006
Trofimov, V. V.; Fomenko, A. T.
1994
A topological invariant which roughly classifies integrable strictly nondegenerate Hamiltonians on four-dimensional symplectic manifolds. Zbl 0778.58023
Fomenko, A. T.
1991
Algorithmic and computer methods in three-dimensional topology. Zbl 0748.57005
Matveev, S. V.; Fomenko, A. T.
1991
Recursion formulas for the Lie integral. Zbl 0743.58007
Chacon, R. V.; Fomenko, A. T.
1991
Minimal surfaces and the Plateau problem. (Minimal’nye poverkhnosti i problema Plato). Zbl 0617.53001
Dao Chong Tkhi; Fomenko, A. T.
1987
The integration of Hamiltonian systems with non-commutative symmetries. Zbl 0473.58015
Mishchenko, A. S.; Fomenko, A. T.
1981
Integrability of Euler equations on semisimple Lie algebras. Zbl 0517.58024
Mishchenko, A. S.; Fomenko, A. T.
1982
The topology of integral submanifolds of completely integrable Hamiltonian systems. Zbl 0667.58022
Brailov, A. V.; Fomenko, A. T.
1989
Minimal compacta in Riemannian manifolds and Reifenberg’s conjecture. Zbl 0282.49040
Fomenko, A. T.
1973
Bordism theory of integrable nondegenerate Hamiltonian systems with two degrees of freedom. A new topological invariant of multi-dimensional integrable systems. Zbl 0746.58037
Fomenko, A. T.
1991
A bordism theory for integrable nondegenerate Hamiltonian systems with two degrees of freedom. A new topological invariant of higher-dimensional integrable systems. Zbl 0783.58035
Fomenko, A. T.
1991
Variational principles in topology. Multidimensional minimal surface theory. Transl. from the Russian by O. Efimov. Rev. translation. Zbl 0697.49044
Fomenko, A. T.
1990
Round Morse functions and isoenergy surfaces of integrable Hamiltonian systems. Zbl 0673.58023
Matveev, S. V.; Fomenko, A. T.; Sharko, V. V.
1989
Elements of differential geometry and topology. Textbook. (Ehlementy differentsial’noj geometrii i topologii. Uchebnoe posobie). Zbl 0628.53002
Novikov, S. P.; Fomenko, A. T.
1987
Dynamical systems on the orbits of linear representations of Lie groups and the complete integrability of certain hydrodynamical systems. Zbl 0521.58031
Trofimov, V. V.; Fomenko, A. T.
1983
Géométrie contemporaine. Méthodes et applications. Deuxième partie: Géométrie et topologie des variates. Traduit du russe par Vladimir Kotliar. Zbl 0502.53003
Dubrovin, B.; Novikov, S.; Fomenko, A.
1982
Homotopical topology. Translated from the Russian. 2nd edition. Zbl 1346.55001
Fomenko, Anatoly; Fuchs, Dmitry
2016
The geodesic flow of an ellipsoid is orbitally equivalent to the Euler integrable case in the dynamics of a rigid body. Zbl 0872.58036
Bolsinov, A. V.; Fomenko, A. T.
1994
Orbital equivalence of integrable Hamiltonian systems with two degrees of freedom. A classification theorem. II. Zbl 0868.58026
Bolsinov, A. V.; Fomenko, A. T.
1994
Integrable geodesic flows on the sphere, generated by Goryachev-Chaplygin and Kowalewski systems in the dynamics of a rigid body. Zbl 0835.70008
Bolsinov, A. V.; Fomenko, A. T.
1994
Variational problems in topology. The geometry of length, area and volume. Transl. from the Russian. Zbl 0716.53004
Fomenko, A. T.
1990
Morse-type theory for integrable Hamiltonian systems with tame integrals. Zbl 0694.58019
Matveev, S. V.; Fomenko, A. T.
1988
Billiards and integrability in geometry and physics. New scope and new potential. Zbl 1429.37030
Fomenko, A. T.; Vedyushkina, V. V.
2019
Topological classification of geodesic flows on revolution 2-surfaces with potential. Zbl 1335.53109
Fomenko, A. T.; Kantonistova, E. O.
2015
Each finite group is the symmetry group of some map (an “atom”-bifurcation). Zbl 1298.37040
Fomenko, A. T.; Kudryavtseva, E. A.
2013
Some new results in topological classification of integrable systems in rigid body dynamics. Zbl 1066.37037
Fomenko, A. T.; Morozov, P. V.
2004
Topological classification of integrable non-degenerate Hamiltonians on a constant energy three-dimensional sphere. Zbl 0721.58022
Nguyen Tien Zung; Fomenko, A. T.
1990
Integrable systems on Lie algebras and symmetric spaces. Transl. from the Russian by A. Karaulov, P. D. Rayfield and A. Weisman. 2nd printing. Zbl 0742.58001
Fomenko, A. T.; Trofimov, V. V.
1989
A Morse type theory for integrable Hamiltonian systems with tame integrals. Zbl 0671.58017
Matveev, S. V.; Fomenko, A. T.
1988
Topological variational problems. Zbl 0679.49001
Fomenko, A. T.
1984
Géométrie contemporaine. Méthodes et applications. Premiere partie: Géométrie des surfaces, des groupes de transformations et des champs. Traduit du russe par Vladimir Kotliar. Zbl 0502.53002
Dubrovin, B.; Novikov, S.; Fomenko, A.
1982
A method for constructing Hamiltonian flows on symmetric spaces and the integrability of some hydrodynamical systems. Zbl 0484.58017
Trofimov, V. V.; Fomenko, A. T.
1980
Integrable geodesic flows on orientable two-dimensional surfaces and topological billiards. Zbl 1436.37068
Vedyushkina, Viktoriya V.; Fomenko, Anatoliĭ T.
2019
Topological methods in the theory of integrable systems. Zbl 1142.37001
Bolsinov, A. V.; Fomenko, A. T.; Oshemkov, A. A.
2006
Lie groups and integrable Hamiltonian systems. Zbl 1013.37047
Brailov, Yury A.; Fomenko, Anatoly T.
2002
Billiards and integrability in geometry and physics. New scope and new potential. Zbl 1429.37030
Fomenko, A. T.; Vedyushkina, V. V.
2019
Integrable geodesic flows on orientable two-dimensional surfaces and topological billiards. Zbl 1436.37068
Vedyushkina, Viktoriya V.; Fomenko, Anatoliĭ T.
2019
Reducing the degree of integrals of Hamiltonian systems by using billiards. Zbl 1423.37055
Vedyushkina, V. V.; Fomenko, A. T.
2019
Implementation of integrable systems by topological, geodesic billiards with potential and magnetic field. Zbl 07127892
Fomenko, A. T.; Vedyushkina, V. V.
2019
Topological billiards, conservation laws and classification of trajectories. Zbl 1426.37047
Fomenko, A. T.; Vedyushkina, V. V.
2019
Modeling nondegenerate bifurcations of closures of solutions for integrable systems with two degrees of freedom by integrable topological billiards. Zbl 1394.37088
Vedyushkina, V. V.; Fomenko, A. T.; Kharcheva, Irina S.
2018
Integrable topological billiards and equivalent dynamical systems. Zbl 1380.37078
Vedyushkina, Viktoriya V.; Fomenko, Anatoly T.
2017
Billiard systems as the models for the rigid body dynamics. Zbl 1362.70005
Fokicheva, Victoria V.; Fomenko, Anatoly T.
2016
Homotopical topology. Translated from the Russian. 2nd edition. Zbl 1346.55001
Fomenko, Anatoly; Fuchs, Dmitry
2016
Integrable billiards model important integrable cases of rigid body dynamics. Zbl 1335.37040
Fokicheva, V. V.; Fomenko, A. T.
2015
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. Zbl 1358.37097
Fomenko, A. T.; Nikolaenko, S. S.
2015
Topological classification of geodesic flows on revolution 2-surfaces with potential. Zbl 1335.53109
Fomenko, A. T.; Kantonistova, E. O.
2015
Algebra and geometry through Hamiltonian systems. Zbl 1362.70023
Fomenko, Anatoly T.; Konyaev, Andrei
2014
Each finite group is the symmetry group of some map (an “atom”-bifurcation). Zbl 1298.37040
Fomenko, A. T.; Kudryavtseva, E. A.
2013
Selected problems in differential geometry and topology. Transl. from the Russian. Zbl 1282.53001
Fomenko, A. T.; Mishchenko, A. S.; Solovyev, Yu. P.
2013
New approach to symmetries and singularities in integrable Hamiltonian systems. Zbl 1248.37050
Fomenko, A. T.; Konyaev, A. Yu.
2012
Symmetries groups of nice Morse functions on surfaces. Zbl 1295.58013
Kudryavtseva, E. A.; Fomenko, A. T.
2012
Hidden symmetries in integrable dynamical systems. Zbl 1332.37038
Fomenko, A. T.
2012
Computer modeling of curves and surfaces. Zbl 1221.37055
Ivanov, A. O.; Tuzhilin, A. A.; Fomenko, A. T.
2011
A short course in differential geometry and topology. Zbl 1160.53002
Fomenko, A. T.; Mishchenko, A. S.
2009
Maximally symmetric cell decompositions of surfaces and their coverings. Zbl 1163.37018
Kudryavtseva, E. A.; Nikonov, I. M.; Fomenko, A. T.
2008
Topological methods in the theory of integrable systems. Zbl 1142.37001
Bolsinov, A. V.; Fomenko, A. T.; Oshemkov, A. A.
2006
Integrable Hamiltonian systems. Geometry, topology, classification. Translated from the 1999 Russian original. Zbl 1056.37075
Bolsinov, A. V.; Fomenko, A. T.
2004
Some new results in topological classification of integrable systems in rigid body dynamics. Zbl 1066.37037
Fomenko, A. T.; Morozov, P. V.
2004
Lie groups and integrable Hamiltonian systems. Zbl 1013.37047
Brailov, Yury A.; Fomenko, Anatoly T.
2002
Riemannian geometry. Zbl 1032.53029
Trofimov, V. V.; Fomenko, A. T.
2002
The method of loop molecules and the topology of the Kovalevskaya top. Zbl 0983.37068
Bolsinov, A. V.; Richter, P. H.; Fomenko, A. T.
2000
Integrable geodesic flows on two-dimensional surfaces. Zbl 1042.37042
Bolsinov, A. V.; Fomenko, A. T.
2000
Integrable Hamiltonian systems. Geometry, topology, classification. Vol. 1, 2. Zbl 1053.37518
Bolsinov, A. V.; Fomenko, A. T.
1999
Differential geometry and topology. Complemented chapters. 2nd revised ed. Zbl 0955.53001
Fomenko, A. T.
1999
Two-dimensional Riemannian metrics with integrable geodesic flows. Local and global geometry. Zbl 0917.58031
Bolsinov, A. V.; Matveev, V. S.; Fomenko, A. T.
1998
Algorithmic and computer methods in three-dimensional topology. 2nd ed., rev. and co. Zbl 0906.57001
Matveev, S. V.; Fomenko, A. T.
1998
Orbital isomorphism between two classical integrable systems. Zbl 0904.58024
Bolsinov, A. V.; Fomenko, A. T.
1998
Tensor and vector analysis. Geometry, mechanics and physics. Zbl 0913.00022
Fomenko, A. T. (ed.); Manturov, O. V. (ed.); Trofimov, V. V. (ed.)
1998
Algorithmic and computer methods for three-manifolds. Transl. from the Russian by M. Tsaplina and M. Hazewinkel. Zbl 0885.57009
Fomenko, A. T.; Matveev, S. V.
1997
Introduction to the topology of integrable Hamiltonian systems. Zbl 0908.58026
Bolsinov, A. V.; Fomenko, A. T.
1997
Topological modeling for visualization. Zbl 1120.37300
Fomenko, A. T.; Kunii, T. L.
1997
On dimension of the space of integrable Hamiltonian systems with two degrees of freedom. Zbl 1073.37532
Bolsinov, A. V.; Fomenko, A. T.
1997
Methods for the mathematical analysis of historical texts. Applications to chronology. (Recognition and dating of dependent texts, statistical ancient chronology, and the statistics of ancient astronomical records). With a preface by A. N. Shiryaev. With appendices by S. T. Rachev, the author, N. S. Kellin, L. E. Morozova, B. E. Brodskii, B. S. Darkhovskii, G. V. Nosovskii, V. P. Fomenko and T. G. Fomenko. 2nd ed., compl. and rev. Zbl 0918.00006
Fomenko, A. T.
1996
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. Zbl 0855.58046
Bolsinov, A. V.; Fomenko, A. T.
1996
Algebra and geometry of integrable Hamiltonian differential equations. Zbl 0858.58026
Trofimov, V. V.; Fomenko, A. T.
1995
The Maupertuis principle and geodesic flows on the sphere arising from integrable cases in the dynamics of a rigid body. Zbl 0881.58031
Bolsinov, A. V.; Kozlov, V. V.; Fomenko, A. T.
1995
Symplectic geometry. 2nd ed. Zbl 0873.58031
Fomenko, A. T.
1995
Orbital classification of geodesic flows on two-dimensional ellipsoids. The Jacobi problem is orbitally equivalent to the integrable Euler case in rigid body dynamics. Zbl 0878.58036
Bolsinov, A. V.; Fomenko, A. T.
1995
Orbital invariants of integrable Hamiltonian systems. The case of simple systems. Orbital classification of systems of Euler type in rigid body dynamics. Zbl 0840.58022
Bolsinov, A. V.; Fomenko, A. T.
1995
Orbital equivalence of integrable Hamiltonian systems with two degrees of freedom. A classification theorem. I. Zbl 0828.58020
Bolsinov, A. V.; Fomenko, A. T.
1994
Geometric and algebraic mechanisms of the integrability of Hamiltonian systems on homogeneous spaces and Lie algebras. Zbl 0797.58006
Trofimov, V. V.; Fomenko, A. T.
1994
The geodesic flow of an ellipsoid is orbitally equivalent to the Euler integrable case in the dynamics of a rigid body. Zbl 0872.58036
Bolsinov, A. V.; Fomenko, A. T.
1994
Orbital equivalence of integrable Hamiltonian systems with two degrees of freedom. A classification theorem. II. Zbl 0868.58026
Bolsinov, A. V.; Fomenko, A. T.
1994
Integrable geodesic flows on the sphere, generated by Goryachev-Chaplygin and Kowalewski systems in the dynamics of a rigid body. Zbl 0835.70008
Bolsinov, A. V.; Fomenko, A. T.
1994
Visual geometry and topology. Transl. from the Russian by M. V.Tsaplina. Zbl 0802.58001
Fomenko, Anatolij T.
1994
Orbital classification of simple integrable Hamiltonian systems on three- dimensional constant-energy surfaces. Zbl 0820.58017
Bolsinov, A. V.; Fomenko, A. T.
1993
Trajectory classification of integrable systems of Euler type in the dynamics of a rigid body. Zbl 0820.58029
Bolsinov, A. V.; Fomenko, A. T.
1993
Minimal surfaces. Zbl 0777.00011
Fomenko, A. T. (ed.)
1993
Modern geometry - methods and applications. Part I. The geometry of surfaces, transformation groups, and fields. Transl. by Robert G. Burns. 2nd ed. Zbl 0751.53001
Dubrovin, B. A.; Fomenko, A. T.; Novikov, S. P.
1992
A topological invariant and a criterion for equivalence of integrable Hamiltonian systems with two degrees of freedom. Zbl 0723.58024
Fomenko, A. T.; Zieschang, H.
1991
Topological classification of all integrable Hamiltonian differential equations of general type with two degrees of freedom. Zbl 0753.58014
Fomenko, A. T.
1991
The theory of invariants of multidimensional integrable Hamiltonian systems (with arbitrary many degrees of freedom). Molecular table of all integrable systems with two degrees of freedom. Zbl 0746.58036
Fomenko, A. T.
1991
Elements of the geometry and topology of minimal surfaces in three-dimensional space. Transl. from the Russian by E. J. F. Primrose. Transl. ed. by Simeon Ivanov. Zbl 0745.53001
Fomenko, A. T.; Tuzhilin, A. A.
1991
A topological invariant which roughly classifies integrable strictly nondegenerate Hamiltonians on four-dimensional symplectic manifolds. Zbl 0778.58023
Fomenko, A. T.
1991
Algorithmic and computer methods in three-dimensional topology. Zbl 0748.57005
Matveev, S. V.; Fomenko, A. T.
1991
Recursion formulas for the Lie integral. Zbl 0743.58007
Chacon, R. V.; Fomenko, A. T.
1991
Bordism theory of integrable nondegenerate Hamiltonian systems with two degrees of freedom. A new topological invariant of multi-dimensional integrable systems. Zbl 0746.58037
Fomenko, A. T.
1991
A bordism theory for integrable nondegenerate Hamiltonian systems with two degrees of freedom. A new topological invariant of higher-dimensional integrable systems. Zbl 0783.58035
Fomenko, A. T.
1991
Topological classification of integrable nondegenerate Hamiltonians on the isoenergy three-dimensional sphere. Zbl 0744.58033
Fomenko, A. T.; Nguyen Tien Zung
1991
Topological classification of integrable systems. Transl. ed. by A. B. Sossinsky. Zbl 0741.00026
Fomenko, A. T. (ed.)
1991
A topological invariant roughly classifying integrable strict non- degenerate Hamiltonians on four-dimensional symplectic manifolds. Zbl 0746.58029
Fomenko, A. T.
1991
Stokes’ formula for Lie algebra valued connection and curvature forms. Zbl 0741.53021
Chacon, R. V.; Fomenko, A. T.
1991
Theory of rough classification of integrable nondegenerate Hamiltonian differential equations on four-dimensional manifolds. Application to classical mechanics. Zbl 0744.58032
Fomenko, A. T.
1991
Statistical analysis of the star catalogue “Almagest”. Zbl 0731.01002
Kalashnikov, V. V.; Nosovskij, G. V.; Fomenko, A. T.
1991
Topological invariant and a criterion for equivalence of integrable Hamiltonian systems with two degrees of freedom. Zbl 0705.58023
Fomenko, A. T.; Zieschang, H.
1990
Modern geometry - methods and applications. Part III. Introduction to homology theory. Transl. from the Russian by Robert G. Burns. Zbl 0703.55001
Dubrovin, B. A.; Fomenko, A. T.; Novikov, S. P.
1990
Topological classification of integrable Hamiltonian systems with two degrees of freedom. List of systems of small complexity. Zbl 0705.58025
Bolsinov, A. V.; Matveev, S. V.; Fomenko, A. T.
1990
Topological classification of integrable Hamiltonian systems with two degrees of freedom. List of systems of small complexity. Zbl 0696.58019
Bolsinov, A. V.; Matveev, S. V.; Fomenko, A. T.
1990
Variational principles in topology. Multidimensional minimal surface theory. Transl. from the Russian by O. Efimov. Rev. translation. Zbl 0697.49044
Fomenko, A. T.
1990
Variational problems in topology. The geometry of length, area and volume. Transl. from the Russian. Zbl 0716.53004
Fomenko, A. T.
1990
Topological classification of integrable non-degenerate Hamiltonians on a constant energy three-dimensional sphere. Zbl 0721.58022
Nguyen Tien Zung; Fomenko, A. T.
1990
Basic elements of differential geometry and topology. Transl. from the Russian by M. V. Tsaplina. Zbl 0711.53001
Novikov, S. P.; Fomenko, A. T.
1990
Statistical analysis and dating of the observations on which Ptolemy’s “Almagest” star catalogue is based. Zbl 0734.62111
Fomenko, A. T.; Kalashnikov, V. V.; Nosovskij, G. V.
1990
Exact round Morse functions, inequalities of Morse type and integrals of Hamiltonian systems. Zbl 0732.58012
Fomenko, A. T.; Sharko, V. V.
1990
Recursion relations for homogeneous terms of a convergent series of the logarithm of a multiplicative integral on Lie groups. Zbl 0732.22005
Fomenko, A. T.; Chakon, R. V.
1990
The Plateau problem. Part I: Historical survey. Part II: The present state of the theory. Transl. from the Russian by Oleg Efimov. Zbl 0729.53001
Fomenko, A. T.
1990
A course in homotopic topology. Textbook. Zbl 0675.55001
Fomenko, A. T.; Fuks, D. B.
1989
The symplectic topology of completely integrable Hamiltonian systems. Zbl 0694.58012
Fomenko, A. T.
1989
Symplectic topology of completely integrable Hamiltonian systems. Zbl 0677.58023
Fomenko, A. T.
1989
On typical topological properties of integrable Hamiltonian systems. Zbl 0667.58014
Fomenko, A. T.; Zieschang, H.
1989
The topology of integral submanifolds of completely integrable Hamiltonian systems. Zbl 0667.58022
Brailov, A. V.; Fomenko, A. T.
1989
Round Morse functions and isoenergy surfaces of integrable Hamiltonian systems. Zbl 0673.58023
Matveev, S. V.; Fomenko, A. T.; Sharko, V. V.
1989
Integrable systems on Lie algebras and symmetric spaces. Transl. from the Russian by A. Karaulov, P. D. Rayfield and A. Weisman. 2nd printing. Zbl 0742.58001
Fomenko, A. T.; Trofimov, V. V.
1989
Exact circular Morse functions, Morse-type inequalities and integrals of Hamiltonian systems. Zbl 0699.58024
Fomenko, A. T.; Sharko, V. V.
1989
When was Ptolemy’s star catalogue in ‘Almagest’ compiled in reality? Statistical analysis. Zbl 0696.01002
Fomenko, A. T.; Kalashnikov, V. V.; Nosovskij, G. V.
1989
Visual and hidden symmetry in geometry. Zbl 0714.53001
Fomenko, A. T.
1989
Integrability and nonintegrability in geometry and mechanics. Transl. from the Russian by M. V. Tsaplina. Zbl 0675.58018
Fomenko, A. T.
1988
Constant energy surfaces of Hamiltonian systems, enumeration of three- dimensional manifolds in increasing order of complexity, and computation of volumes of closed hyperbolic manifolds. Zbl 0671.58008
Matveev, S. V.; Fomenko, A. T.
1988
Symplectic geometry. Methods and applications. Zbl 0751.53002
Fomenko, A. T.
1988
Topological invariants of Liouville integrable Hamiltonian systems. Zbl 0697.58021
Fomenko, A. T.
1988
On typical topological properties of integrable Hamiltonian systems. Zbl 0647.58018
Fomenko, A. T.; Zieschang, H.
1988
Non-invariant symplectic group structures and Hamiltonian flows on symmetric spaces. Zbl 0659.58018
Trofimov, V. V.; Fomenko, A. T.
1988
Morse-type theory for integrable Hamiltonian systems with tame integrals. Zbl 0694.58019
Matveev, S. V.; Fomenko, A. T.
1988
A Morse type theory for integrable Hamiltonian systems with tame integrals. Zbl 0671.58017
Matveev, S. V.; Fomenko, A. T.
1988
...and 66 more Documents
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#### Cited in 266 Serials

 75 Journal of Mathematical Sciences (New York) 52 Journal of Geometry and Physics 47 Moscow University Mathematics Bulletin 45 Regular and Chaotic Dynamics 39 Communications in Mathematical Physics 38 Mathematical Notes 36 Journal of Mathematical Physics 34 Theoretical and Mathematical Physics 25 Physica D 22 Topology and its Applications 20 Advances in Mathematics 17 Functional Analysis and its Applications 17 Siberian Mathematical Journal 16 Doklady Mathematics 15 Sbornik: Mathematics 14 Journal of Soviet Mathematics 13 Journal of Mathematical Analysis and Applications 13 Acta Applicandae Mathematicae 13 Proceedings of the Steklov Institute of Mathematics 12 Russian Mathematics 11 Nuclear Physics. B 11 Transactions of the American Mathematical Society 11 Annals of Global Analysis and Geometry 11 Annals of Physics 11 Russian Journal of Mathematical Physics 10 Journal of Applied Mathematics and Mechanics 10 Letters in Mathematical Physics 10 Physics Letters. A 10 Discrete & Computational Geometry 9 Differential Geometry and its Applications 9 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 9 Chebyshevskiĭ Sbornik 8 International Journal of Theoretical Physics 8 Reports on Mathematical Physics 8 Chaos, Solitons and Fractals 8 Annales de l’Institut Fourier 8 Journal of Algebra 8 Lobachevskii Journal of Mathematics 8 Differential Equations 7 Ukrainian Mathematical Journal 7 Duke Mathematical Journal 7 Journal of Differential Equations 7 Proceedings of the American Mathematical Society 7 International Journal of Geometric Methods in Modern Physics 6 Russian Mathematical Surveys 6 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 6 Journal of Functional Analysis 6 Manuscripta Mathematica 6 Mathematische Annalen 6 Geometric and Functional Analysis. GAFA 6 Bulletin of the American Mathematical Society. New Series 6 Russian Physics Journal 6 Qualitative Theory of Dynamical Systems 6 Algebraic & Geometric Topology 6 Journal of Geometric Mechanics 5 Mathematische Zeitschrift 5 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 5 The Journal of Geometric Analysis 5 Journal of Nonlinear Science 5 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Computer Methods in Applied Mechanics and Engineering 4 Discrete Mathematics 4 Mathematics of Computation 4 Compositio Mathematica 4 European Journal of Combinatorics 4 Computational Geometry 4 Automation and Remote Control 4 Indagationes Mathematicae. New Series 4 Calculus of Variations and Partial Differential Equations 4 St. Petersburg Mathematical Journal 4 Discrete and Continuous Dynamical Systems 4 Journal of High Energy Physics 4 Journal of Nonlinear Mathematical Physics 3 Archive for Rational Mechanics and Analysis 3 Communications in Algebra 3 Journal of Statistical Physics 3 Physics Reports 3 Prikladnaya Matematika i Mekhanika 3 Inventiones Mathematicae 3 Journal of Pure and Applied Algebra 3 Systems & Control Letters 3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 Journal of the American Mathematical Society 3 Science in China. Series A 3 Linear Algebra and its Applications 3 Journal of Knot Theory and its Ramifications 3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 3 Advances in Applied Clifford Algebras 3 Bulletin des Sciences Mathématiques 3 Acta Mathematica Sinica. English Series 3 Communications in Nonlinear Science and Numerical Simulation 3 Journal of Dynamical and Control Systems 3 Central European Journal of Mathematics 3 Complex Analysis and Operator Theory 3 Journal of Noncommutative Geometry 3 Journal of Physics A: Mathematical and Theoretical 3 $$p$$-Adic Numbers, Ultrametric Analysis, and Applications 3 Nelineĭnaya Dinamika 2 Computers & Mathematics with Applications 2 Communications on Pure and Applied Mathematics ...and 166 more Serials
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#### Cited in 60 Fields

 441 Dynamical systems and ergodic theory (37-XX) 288 Differential geometry (53-XX) 262 Mechanics of particles and systems (70-XX) 160 Manifolds and cell complexes (57-XX) 143 Global analysis, analysis on manifolds (58-XX) 104 Quantum theory (81-XX) 102 Partial differential equations (35-XX) 87 Nonassociative rings and algebras (17-XX) 70 Ordinary differential equations (34-XX) 54 Fluid mechanics (76-XX) 50 Functional analysis (46-XX) 49 Algebraic topology (55-XX) 41 Algebraic geometry (14-XX) 41 Calculus of variations and optimal control; optimization (49-XX) 40 Relativity and gravitational theory (83-XX) 38 Topological groups, Lie groups (22-XX) 33 Statistical mechanics, structure of matter (82-XX) 31 Mechanics of deformable solids (74-XX) 26 Numerical analysis (65-XX) 25 Group theory and generalizations (20-XX) 24 Convex and discrete geometry (52-XX) 23 Computer science (68-XX) 22 Operator theory (47-XX) 21 Combinatorics (05-XX) 18 $$K$$-theory (19-XX) 18 Systems theory; control (93-XX) 16 Functions of a complex variable (30-XX) 16 Several complex variables and analytic spaces (32-XX) 16 Optics, electromagnetic theory (78-XX) 13 Geometry (51-XX) 12 Linear and multilinear algebra; matrix theory (15-XX) 11 Associative rings and algebras (16-XX) 9 Measure and integration (28-XX) 9 General topology (54-XX) 8 History and biography (01-XX) 8 Probability theory and stochastic processes (60-XX) 7 Mathematical logic and foundations (03-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Number theory (11-XX) 6 Commutative algebra (13-XX) 6 Astronomy and astrophysics (85-XX) 6 Operations research, mathematical programming (90-XX) 6 Biology and other natural sciences (92-XX) 5 General and overarching topics; collections (00-XX) 5 Category theory; homological algebra (18-XX) 5 Potential theory (31-XX) 5 Special functions (33-XX) 5 Difference and functional equations (39-XX) 4 Abstract harmonic analysis (43-XX) 3 Real functions (26-XX) 3 Approximations and expansions (41-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Integral equations (45-XX) 3 Statistics (62-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Geophysics (86-XX) 3 Information and communication theory, circuits (94-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 1 Field theory and polynomials (12-XX) 1 Sequences, series, summability (40-XX)

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