Anatoliĭ Timofeevich Fomenko

Anatoliĭ Timofeevich Fomenko's AcademicInfluence.com Rankings

Mathematics

#7140

World Rank

#9766

Historical Rank

Geometry

#156

World Rank

#229

Historical Rank

Measure Theory

#1897

World Rank

#2312

Historical Rank

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Mathematics

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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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Published Works

Anatoliĭ Timofeevich Fomenko's AcademicInfluence.com Rankings