Anatoliĭ Timofeevich Fomenko
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Why Is Anatoliĭ Timofeevich Fomenko Influential?
(Suggest an Edit or Addition)Anatoliĭ Timofeevich Fomenko's Published Works
Number of citations in a given year to any of this author's works
Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author
Published Works
- Modern geometry--methods and applications (1984) (1154)
- Integrable Hamiltonian Systems: Geometry, Topology, Classification (2004) (418)
- Generalized Liouville method of integration of Hamiltonian systems (1978) (301)
- The geometry of surfaces, transformation groups, and fields (1984) (251)
- Euler equations on finite-dimensional Lie groups (1978) (243)
- THE INDEX OF ELLIPTIC OPERATORS OVER C*-ALGEBRAS (1980) (239)
- Modern Geometry-Methods and Applications(Part II. The Geometry and Topology of Manifolds) (2010) (182)
- Topological classification of integrable Hamiltonian systems with two degrees of freedom. List of systems of small complexity (1990) (140)
- A TOPOLOGICAL INVARIANT AND A CRITERION FOR THE EQUIVALENCE OF INTEGRABLE HAMILTONIAN SYSTEMS WITH TWO DEGREES OF FREEDOM (1991) (133)
- The Topology of Surfaces of Constant Energy in Integrable Hamiltonian Systems, and Obstructions to Integrability (1987) (128)
- The symplectic topology of completely integrable Hamiltonian systems (1989) (114)
- Algorithmic and Computer Methods for Three-Manifolds (1997) (114)
- Integrability and Nonintegrability in Geometry and Mechanics (1988) (105)
- THE PROBLEM OF DISCRIMINATING ALGORITHMICALLY THE STANDARD THREE-DIMENSIONAL SPHERE (1974) (103)
- Constant energy surfaces of Hamiltonian systems, enumeration of three-dimensional manifolds in increasing order of complexity, and computation of volumes of closed hyperbolic manifolds (1988) (94)
- Integrable systems on Lie algebras and symmetric spaces (1988) (80)
- The method of loop molecules and the topology of the Kovalevskaya top (2000) (77)
- The Maupertuis principle and geodesic flows on the sphere arising from integrable cases in the dynamics of a rigid body (1995) (71)
- On Typical Topological Properties of Integrable Hamiltonian Systems (1989) (69)
- Topological invariants of Liouville integrable Hamiltonian systems (1988) (69)
- Two-dimensional Riemannian metrics with integrable geodesic flows. Local and global geometry (1998) (65)
- A course of differential geometry and topology (1988) (62)
- Visual geometry and topology (1994) (60)
- Topological Classification of All Integrable Hamiltonian Differential Equations of General Type With Two Degrees of Freedom (1991) (58)
- Maximally symmetric cell decompositions of surfaces and their coverings (2008) (56)
- The Theory of Invariants of Multidimensional Integrable Hamiltonian Systems (1991) (54)
- Elements of the geometry and topology of minimal surfaces in three-dimensional space (2005) (53)
- Liouville integrability of Hamiltonian systems on Lie algebras (1984) (51)
- Minimal Surfaces, Stratified Multivarifolds, and the Plateau Problem (1991) (48)
- Topological classification of integrable systems (1991) (48)
- Differential geometry and topology (1987) (47)
- New approach to symmetries and singularities in integrable Hamiltonian systems (2012) (47)
- Topological Methods in the Theory of Integrable Systems (2006) (46)
- THE TOPOLOGY OF INTEGRAL SUBMANIFOLDS OF COMPLETELY INTEGRABLE HAMILTONIAN SYSTEMS (1989) (46)
- Symmetries groups of nice Morse functions on surfaces (2012) (45)
- Integrable Geodesic Flows on Two-Dimensional Surfaces (1999) (45)
- Orbital equivalence of integrable Hamiltonian systems with two degrees of freedom (1995) (42)
- On the integration of the Euler equations on semisimple Lie algebras (1976) (41)
- ON THE TOPOLOGY OF 3-DIMENSIONAL MANIFOLDS ARISING IN HAMILTONIAN-MECHANICS (1987) (41)
- Integrability of Euler Equations on Semisimple Lie Algebras (1982) (39)
- Orbital classification of geodesic flows on two-dimensional ellipsoids. The Jacobi problem is orbitally equivalent to the integrable Euler case in rigid body dynamics (1995) (35)
- A BORDISM THEORY FOR INTEGRABLE NONDEGENERATE HAMILTONIAN SYSTEMS WITH TWO DEGREES OF FREEDOM. A NEW TOPOLOGICAL INVARIANT OF HIGHER-DIMENSIONAL INTEGRABLE SYSTEMS (1992) (35)
- The geometry and topology of manifolds (1985) (34)
- A topological invariant which roughly classifies integrable strictly nondegenerate Hamiltonians on four-dimensional symplectic manifolds (1991) (33)
- Morse-type theory for integrable Hamiltonian systems with tame integrals (1988) (32)
- ROUND MORSE FUNCTIONS AND ISOENERGY SURFACES OF INTEGRABLE HAMILTONIAN SYSTEMS (1989) (29)
- Recursion formulas for the Lie integral (1991) (26)
- Basic Elements of Differential Geometry and Topology (1990) (24)
- Variational Problems in Topology (1990) (23)
- 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 (2015) (21)
- The present state of the theory (1990) (21)
- Variational Principles in Topology (1990) (20)
- Dynamical systems on the orbits of linear representations of Lie groups and the complete integrability of certain hydrodynamical systems (1983) (20)
- MINIMAL COMPACTA IN RIEMANNIAN MANIFOLDS AND REIFENBERG'S CONJECTURE (1972) (20)
- INTEGRATION OF EULERIAN EQUATIONS ON LIE SEMISIMPLE ALGEBRAS (1976) (20)
- ON SYMPLECTIC STRUCTURES AND INTEGRABLE SYSTEMS ON SYMMETRIC SPACES (1982) (19)
- Topological classification of integrable nondegenerate Hamiltonians on the isoenergy three-dimensional sphere (1991) (17)
- ORBITS OF SMOOTH FUNCTIONS ON 2-TORUS AND THEIR HOMOTOPY TYPES (2015) (16)
- Integrable geodesic flows on the sphere, generated by Goryachev-Chaplygin and Kowalewski systems in the dynamics of a rigid body (1994) (16)
- A short course in differential geometry and topology (2009) (16)
- Recursion relations for homogeneous terms of a convergent series of the logarithm of a multiplicative integral on Lie groups (1990) (16)
- The Multidimensional Plateau Problem in Riemannian Manifolds (1972) (16)
- Functions on Manifolds (2019) (14)
- Qualitative geometrical theory of integrable systems. classification of isoenergetic surfaces and bifurcation of liouville tori at the critical energy values (1988) (13)
- Stokes' formula for Lie algebra valued connection and curvature forms (1991) (13)
- Topology of Foliations Generated by Morse Functions on Two-Dimensional Surfaces (2000) (12)
- Each finite group is a symmetry group of some map (an “Atom”-bifurcation) (2013) (12)
- Problems in Differential Geometry and Topology (1985) (11)
- Symplectic topology of integrable dynamical systems. Rough topological classification of classical cases of integrability in the dynamics of a heavy rigid body (1999) (10)
- The jump of the second derivative of the Moon's elongation (1981) (9)
- SOME NEW RESULTS IN TOPOLOGICAL CLASSIFICATION OF INTEGRABLE SYSTEMS IN RIGID BODY DYNAMICS (2004) (9)
- A METHOD OF DUPLICATE RECOGNITION AND SOME APPLICATIONS (1981) (9)
- The Theory of Surfaces (1984) (8)
- Geometry in Regions of a Space. Basic Concepts (1984) (8)
- Geometry of Poisson brackets and methods of Liouville integration of systems on symmetric spaces (1987) (8)
- A NEW EMPIRICAL-STATISTICAL PROCEDURE FOR TEXT ORDERING AND ITS APPLICATIONS TO THE PROBLEMS OF DATING (1983) (7)
- Multi-dimensional variational methods in the topology of extremals (1981) (7)
- Geometric variational problems (1975) (7)
- The geodesic-flow on the ellipsoid is orbitally equivalent to the euler case in rigid-body dynamics (1994) (7)
- LAGRANGIAN MANIFOLDS AND MASLOV INDEX IN THE THEORY OF MINIMAL-SURFACES (1988) (7)
- Exact topological classification of Hamiltonian flows on smooth two-dimensional surfaces (1999) (7)
- Singularities of integrable Liouville systems, reduction of integrals to lower degree and topological billiards: Recent results (2019) (6)
- Variational Principles of Topology: Multidimensional Minimal Surface Theory (2011) (6)
- The integrability of some Hamiltonian systems (1983) (6)
- 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 (1996) (6)
- Topological Classification of Geodesic Flows on Revolution 2-Surfaces with Potential (2015) (5)
- Orbital invariants of integrable Hamiltonian systems. The case of simple systems. Orbital classification of systems of Euler type in rigid body dynamics (1995) (5)
- Anatolii Mikhailovich Stepin (on his 60th birthday) (2001) (5)
- COMMUNICATIONS OF THE MOSCOW MATHEMATICAL SOCIETY: Trajectory classification of integrable systems of Euler type in the dynamics of a rigid body (1993) (5)
- Quantum duality principle for coisotropic subgroups and Poisson quotients (2006) (5)
- REALIZATION OF CYCLES IN COMPACT SYMMETRIC SPACES BY COMPLETELY GEODESIC SUBMANIFOLDS (1970) (5)
- Trajectory Classification of Integrable Geodesic Flows on Two-Dimensional Surfaces (2000) (5)
- Liouville Foliations of Topological Billiards with Slipping (2021) (5)
- Invariant portrait of Hamiltonian integrable in Liouville sense (1988) (4)
- Visual and hidden symmetry in geometry (1989) (4)
- EXISTENCE OF MINIMAL COMPACTA WITH GIVEN HOMOLOGICAL PROPERTIES, AND THEIR REGULARITY ALMOST EVERYWHERE (1969) (4)
- Geometrical and Statistical Methods of Analysis of Star Configurations Dating Ptolemy's Almagest (1993) (4)
- MULTIDIMENSIONAL PLATEAU PROBLEM AND SINGULAR POINTS OF MINIMAL COMPACTA (1970) (4)
- Statistical estimation of chronological nearness of historical texts (1986) (3)
- Symplectic lie group actions (1979) (3)
- Topological billiards, conservation laws and classification of trajectories (2019) (3)
- ON MINIMAL VOLUMES OF TOPOLOGICAL GLOBALLY MINIMAL SURFACES IN COBORDISMS (1982) (3)
- Force Evolutionary Billiards and Billiard Equivalence of the Euler and Lagrange Cases (2021) (3)
- Exact round morse functions, Morse-type inequalities and integrals of Hamiltonian systems (1989) (3)
- Existence and almost everywhere regularity of minimal compacts with given homological properties (1969) (3)
- Algebraic structure of certain integrable hamiltonian systems (1984) (3)
- Algebraic properties of some integrable Hamiltonian systems (1984) (3)
- BOTT PERIODICITY FROM THE POINT OF VIEW OF AN n-DIMENSIONAL DIRICHLET FUNCTIONAL (1971) (3)
- ON COMBINATORIAL ANALOGS OF THE GROUP OF DIFFEOMORPHISMS OF THE CIRCLE (2017) (2)
- Orbital Isomorphism Between Two Classical Integrable Systems (1998) (2)
- Examples of Manifolds (1985) (2)
- Empirico-Statistical Analysis of Narrative Material and its Applications to Historical Dating (1993) (2)
- The dating of Ptolemy's Almagest based on the coverings of the stars and on lunar eclipses (1992) (2)
- A New Topological Invariant of Hamiltonian Systems of Liouville-Integrable Differential Equations. An Invariant Portrait of Integrable Equations and Hamiltonians (1988) (2)
- Solution of the Plateau Problem in Classes of Mappings of Spectra of Manifolds with Fixed Boundary. Construction of Globally Minimal Surfaces in Variational Classes h (A,L,L’) and h (A, $$\tilde L $$ ) (1990) (2)
- Exact round morse functions, inequalities of morse type and integrals of Hamiltonian systems (1990) (2)
- Tensor and Vector Analysis: Geometry, Mechanics and Physics (1998) (2)
- STATISTICAL ANALYSIS OF THE STAR CATALOGUE ALMAGEST (1991) (1)
- A new empirical statistical methodology for detection of parallelisms and dating of duplicates (1986) (1)
- The multidimensional plateau problem in Riemannian varieties (1973) (1)
- SYMMETRIES OF SOAP FILMS (1986) (1)
- Homology and Cohomology. Computational Recipes (1990) (1)
- Computer modeling of curves and surfaces (2011) (1)
- The Elements of the Calculus of Variations (1984) (1)
- Critical Points of Smooth Functions and Homology Theory (1990) (1)
- PETR KONSTANTINOVICH RASHEVSKII (on his seventieth birthday) (1977) (1)
- A criterion for the topological conjugacy of Hamiltonian flows on two-dimensional compact surfaces (1995) (1)
- Empirico-Statistical Methods in Ordering Narrative Texts (1988) (1)
- Special Lecture: Computer Visualization for the Topology of Integrable Cases in Rigid Body Dynamics (1998) (1)
- Tensors: The Algebraic Theory (1984) (1)
- The Differential Calculus of Tensors (1984) (0)
- Methods of Calculation of Topological Invariants of Integrable Hamiltonian Systems (2004) (0)
- Some General Principles of Integration of Hamiltonian Systems of Differential Equations (1988) (0)
- On certain properties of extremals in variational problems (1984) (0)
- Empirico-statistical methods for analysis of narrative and numerical sources with applications to the problems of ancient and medieval history and chronology (1993) (0)
- The Presentation of Three-Dimensional Manifolds by the Identification of Faces of Polyhedra (1997) (0)
- Selected Problems in Differential Geometry and Topology (2012) (0)
- Linear-Quadratic Metrics “Approximate” any Nondegenerate, Integrable Riemannian Metric on the 2-Sphere and the 2-Torus (1993) (0)
- Liouville Classification of Integrable Systems with Two Degrees of Freedom in Four-Dimensional Neighborhoods of Singular Points (2004) (0)
- The Topology of Liouville Foliations in Classical Integrable Cases in Rigid Body Dynamics (2004) (0)
- Multidimensional Plateau Problem on Riemannian Manifolds . On the Problem of the Algorithmical Recognizability of the Standard Three-Dimensional Sphere (2010) (0)
- Chapter 5: The Adams Spectral Sequence (2016) (0)
- Geometrical & Statistical Methods Analysis Star Config (1993) (0)
- Orbital Classifcation of Integrable Systems with Two Degrees of Freedom (2004) (0)
- Cobordisms and Smooth Structures (1990) (0)
- New techniques for comparing the volume functions of historical texts (1989) (0)
- Some Examples of Dynamical Systems and Foliations on Manifolds (1985) (0)
- Chapter 6: K-Theory and Other Extraordinary Cohomology Theories (2016) (0)
- DEFORMATIONS OF FUNCTIONS ON SURFACES BY ISOTOPIC TO THE IDENTITY DIFFEOMORPHISMS (2019) (0)
- The analysis of ancient and medieval records (1994) (0)
- The Topology of Foliations on Two-Dimensional Surfaces Generated by Morse Functions (2004) (0)
- Mathematical statistics and problems of ancient chronology. A new approach (1989) (0)
- Geometry, dynamics and different types of orbits (2014) (0)
- Riemannian Geometry (2002) (0)
- Visual Topology and Variational Problems on Two-Dimensional Surfaces (2005) (0)
- Tensors. Riemannian Geometry (1990) (0)
- Three-Dimensional Manifolds of Constant Energy and Invariants of Integrable Hamiltonian Systems (2018) (0)
- Euler Case in Rigid Body Dynamics and Jacobi Problem About Geodesics on the Ellipsoid. Trajectory Isomorphism (2000) (0)
- Basic Elements of Topology (1990) (0)
- Yevgeny Mikhailovich Nikishin (1995) (0)
- Classifcation of Hamiltonian Flows on Two-Dimensional Surfaces up to Topological Conjugacy (2004) (0)
- Chapter 3: Spectral Sequences of Fibrations (2016) (0)
- Knots and Links (1997) (0)
- Nonintegrability of Certain Classical Hamiltonian Systems (1988) (0)
- A NEW TOPOLOGICAL INVARIANT OF TOPOLOGICAL HAMILTONIAN SYSTEMS OF DIFFERENTIAL EQUATIONS AND APPLICATIONS TO PROBLEMS IN PHYSICS AND MECHANICS (1991) (0)
- Trajectory Classification of Integrable Systems with Two Degrees of Freedom (2000) (0)
- Introduction to homology theory (1990) (0)
- Chapter 4: Cohomology Operations (2016) (0)
- A technique for recognizing duplicates, and some applications (1981) (0)
- The Calculus of Variations in Several Dimensions. Fields and Their Geometric Invariants (1984) (0)
- Symmetries groups of nice Morse functions on surfaces (2012) (0)
- Orbital Classification of Integrable Hamiltonian Systems with Two Degrees of Freedom. The Second Step (2004) (0)
- Manifolds of Small Dimensions (2019) (0)
- The Global Structure of Solutions of Higher-Dimensional Variational Problems (1985) (0)
- The development of the statistical tools (1994) (0)
- Maupertuis Principle and Geodesic Equivalence (2000) (0)
- Chapter 2: Homology (2016) (0)
- MULTIDIMENSIONAL PLATEAU PROBLEM IN EXTRAORDINARY THEORIES OF HOMOLOGIES AND COHOMOLOGIES (1971) (0)
- The Haken Method (1997) (0)
- NORDEN,ALEKSANDR,PETROVICH - OBITUARY (1993) (0)
- VOLUMES OF MINIMAL-SURFACES AND THE CURVATURE TENSOR OF RIEMANNIAN-MANIFOLDS (1988) (0)
- Empirico-Statistical Analysis of Narrative Material and its Applications to Historical Dating: Volume I: The Development of the Statistical Tools (1993) (0)
- Algorithmic Recognition of the Sphere (1997) (0)
- New results in the theory of topological classification of integrable systems (1995) (0)
- Topological Classi fi cation of Integrable Geodesic Flows in a Potential Field on the Torus of Revolution (0)
- Basic Concepts of Differential Geometry (1990) (0)
- Identifying duplicates in chronological lists (the method of frequency histograms for the spread of related names) (1992) (0)
- Recognition of dependences and stratified structures in narrative texts (1989) (0)
- Explicit Calculation of Least Volumes (Absolute Minimum) of Topologically Nontrivial Minimal Surfaces (1990) (0)
- Heegaard Splittings and Heegaard Diagrams (1997) (0)
- Foundational Questions. Essential Facts Concerning Functions on a Manifold. Typical Smooth Mappings (1985) (0)
- STATISTICAL-ANALYSIS OF THE ALMAGEST STAR CATALOG (1990) (0)
- Computers and Visualization in Hyperbolic Three-Dimensional Geometry and Topology (1997) (0)
- Yurii Grigor'evich Borisovich (obituary) (2008) (0)
- Smooth Fibre Bundles (1985) (0)
- The Degree of a Mapping. The Intersection Index of Submanifolds. Applications (1985) (0)
- Rough Liouville Equivalence of Integrable Systems with Two Degrees of Freedom (2000) (0)
- Locally Minimal Closed Surfaces Realizing Nontrivial (Co) Cycles and Elements of Symmetric Space Homotopy Groups (1990) (0)
- Smooth Conjugacy of Hamiltonian Flows on Two-Dimensional Surfaces (2004) (0)
- Minimization of length, area, and volume. Some solved and some unsolved problems in the theory of minimal graphs and surfaces (1993) (0)
- Chapter 1: Homotopy (2016) (0)
- Topology of low-dimensional manifolds and geometry of Hamiltonian systems with applications to physics and mechanics (2003) (0)
- The geometry of moving stellar configurations and the dating of theAlmagest (1991) (0)
- Rough Classification of Integrable Hamiltonians on Four-Dimensional Symplectic Manifolds (1993) (0)
- Surgery along Links (1997) (0)
- Simplest Classical Variational Problems (1990) (0)
- Orientability of Manifolds. The Fundamental Group. Covering Spaces (Fibre Bundles with Discrete Fibre) (1985) (0)
- The Homeotopy Group of a Surface (1997) (0)
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