#1,302

Most Influential Person

Russian mathematician – studied integrable systems and differential equations

According to Wikipedia, Vladimir Igorevich Arnold was a Soviet and Russian mathematician. While he is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable systems, he made important contributions in several areas including dynamical systems theory, algebra, catastrophe theory, topology, algebraic geometry, symplectic geometry, differential equations, classical mechanics, hydrodynamics and singularity theory, including posing the ADE classification problem, since his first main result—the solution of Hilbert's thirteenth problem in 1957 at the age of 19. He co-founded two new branches of mathematics—KAM theory, and topological Galois theory .

- Mathematical Methods of Classical Mechanics (1974) (10805)
- Geometrical Methods in the Theory of Ordinary Differential Equations (1983) (2959)
- Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits (1966) (1440)
- Ordinary Differential Equations (1973) (1368)
- Topological methods in hydrodynamics (1998) (1313)
- SMALL DENOMINATORS AND PROBLEMS OF STABILITY OF MOTION IN CLASSICAL AND CELESTIAL MECHANICS (1963) (948)
- Dynamical Systems III (1987) (460)
- Instability of dynamical systems with several degrees of freedom (1964) (299)
- Singularities of Caustics and Wave Fronts (1990) (283)
- The asymptotic Hopf invariant and its applications (1974) (277)
- Wave front evolution and equivariant Morse lemma (1976) (274)
- On an a priori estimate in the theory of hydrodynamical stability (1966) (255)
- Sur la topologie des écoulements stationnaires des fluides parfaits (1965) (245)
- CRITICAL POINTS OF SMOOTH FUNCTIONS AND THEIR NORMAL FORMS (1975) (240)
- Conditions for nonlinear stability of stationary plane curvilinear flows of an ideal fluid (1965) (234)
- Dynamical Systems III: Mathematical Aspects of Classical and Celestial Mechanics (1989) (227)
- ON MATRICES DEPENDING ON PARAMETERS (1971) (218)
- The cohomology ring of the colored braid group (1969) (218)
- Topological Invariants of Plane Curves and Caustics (1994) (206)
- Singularities of Differentiable Maps, Volume 2 (2012) (193)
- ON MATRICES DEPENDING ON PARAMETERS (1971) (183)
- LECTURES ON BIFURCATIONS IN VERSAL FAMILIES (1972) (183)
- On some topological invariants of algebraic functions (1970) (166)
- The large scale structure of the universe I. General properties. One-and two-dimensional models (1982) (166)
- Mathematics: Frontiers and Perspectives (2000) (160)
- The cohomology ring of the colored braid group (1969) (159)
- Theory of perturbations and asymptotic methods (1972) (153)
- NORMAL FORMS OF FUNCTIONS IN NEIGHBOURHOODS OF DEGENERATE CRITICAL POINTS (1974) (149)
- Plane curves, their invariants, Perestroikas, and classifications (1994) (149)
- Singularity Theory I (1998) (142)
- Differential algebra of Legendrian links (2002) (135)
- Dynamical Systems I (1988) (135)
- Critical points of functions on a manifold with boundary (1978) (133)
- Singularities of Differentiable Maps, Volume 1 (2012) (129)
- Critical Points of Smooth Functions (1975) (123)
- Modes and quasimodes (1972) (120)
- Dynamical systems V. Bifurcation theory and catastrophe theory (1994) (120)
- Local normal forms of functions (1976) (111)
- SINGULARITIES OF SMOOTH MAPPINGS (1968) (111)
- Ordinary differential equations and smooth dynamical systems (1997) (100)
- Arnold's Problems (2008) (98)
- Singularities of systems of rays (1983) (87)
- Dynamics of complexity of intersections (1990) (86)
- Dynamical Systems IV (1987) (85)
- The geometry of spherical curves and the algebra of quaternions (1995) (85)
- Encyclopaedia of Mathematical Sciences (1990) (84)
- REMARKS ON THE STATIONARY PHASE METHOD AND COXETER NUMBERS (1973) (82)
- Mathematical aspects of classical and celestial mechanics (2nd ed.) (1997) (78)
- INDICES OF SINGULAR POINTS OF 1-FORMS ON A MANIFOLD WITH BOUNDARY, CONVOLUTION OF INVARIANTS OF REFLECTION GROUPS, AND SINGULAR PROJECTIONS OF SMOOTH SURFACES (1979) (78)
- Newton-Okounkov bodies, semigroups of integral points, graded algebras and intersection theory (2012) (73)
- The calculus of snakes and the combinatorics of Bernoulli, Euler and Springer numbers of Coxeter groups (1992) (71)
- Hamiltonian nature of the Euler equations in the dynamics of a rigid body and of an ideal fluid (1969) (68)
- Dynamical Systems VII (1994) (63)
- Remarks on the perturbation theory for problems of Mathieu type (1983) (62)
- Singularities of Differentiable Maps, Volume 2: Monodromy and Asymptotics of Integrals (2012) (61)
- Variational principle for three-dimensional steady-state flows of an ideal fluid (1965) (61)
- Bernoulli-Euler updown numbers associated with function singularities, their combinatorics and arithmetics (1991) (61)
- Some remarks on symplectic monodromy of Milnor fibrations (1995) (60)
- Remarks on eigenvalues and eigenvectors of Hermitian matrices, berry phase, adiabatic connections and quantum Hall effect (1995) (60)
- Some unsolved problems in the theory of differential equations and mathematical physics (1989) (54)
- Topological classification of trigonometric polynomials and combinatorics of graphs with an equal number of vertices and edges (1996) (51)
- Huygens and Barrow, Newton and Hooke (1990) (50)
- Instability of dynamical systems with several degrees of freedom (1964) (50)
- Lagrangian manifolds with singularities, asymptotic rays, and the open swallowtail (1981) (49)
- A-graded algebras and continued fractions (1989) (47)
- The Sturm theorems and symplectic geometry (1985) (47)
- On teaching mathematics (1998) (47)
- Polymathematics: Is mathematics a single science or a set of arts? (2000) (46)
- Topological invariants of algebraic functions II (1970) (45)
- "Huygens and Barrow, Newton and Hooke": Pioneers in Mathematical Analysis and Catastrophe Theory from Evolvents to Quasicrystals (1990) (44)
- Mathematical problems in classical physics (1994) (42)
- THE ROLE OF MATHEMATICS IN PHYSICAL SCIENCES (2003) (42)
- Normal forms for functions near degenerate critical points, the Weyl groups of A k , D (1972) (40)
- Topological methods in hydrodynamics Applied Mathematical Sciences 125 (1998) (39)
- Arithmetics of binary quadratic forms, symmetry of their continued fractions and geometry of their de Sitter world (2003) (37)
- Symplectic geometry and topology (2000) (37)
- Cardiac arrhythmias and circle mappingsa) (1991) (36)
- Complex Algebraic Curves (2013) (36)
- Magnetic field in a stationary flow with stretching in Riemannian space (1981) (36)
- Topological problems of the theory of wave propagation (1996) (35)
- Simple Singularities of Curves (1999) (35)
- On some problems in singularity theory (1981) (34)
- Higher Dimensional Continued Fractions (1998) (34)
- Dynamical Systems IV: Symplectic Geometry and its Applications (2010) (33)
- Contact Geometry And Wave Propagation (1989) (32)
- Weak asymptotics for the numbers of solutions of diophantine problems (1999) (31)
- The growth of a magnetic field in a three-dimensional steady incompressible flow (1983) (31)
- From Hilbert's Superposition Problem to Dynamical Systems (2004) (30)
- Remarks on singularities of finite codimension in complex dynamical systems (1969) (30)
- Topological Classification of Morse Functions and Generalisations of Hilbert’s 16-th Problem (2007) (29)
- Introduction to perturbation theory (1989) (29)
- Cardiac arrhythmias and circle mappings(a)). (1991) (29)
- On the number of flattening points on space curves (1995) (28)
- Kolmogorov's Hydrodynamic Attractors (1991) (28)
- Conditions for nonlinear stability of plane steady curvilinear flows of an ideal fluid (1965) (27)
- Remarks on quasicrystallic symmetries (1988) (27)
- Dynamical systems. VI, Singularity theory (1993) (24)
- On some problems in symplectic topology (1988) (23)
- On the differential geometry of infinite-dimensional Lie groups and its application to the hydrodynamics of perfect fluids (1966) (22)
- On the arrangement of ovals of real plane algebraic curves, involutions of four-dimensional smooth manifolds, and the arithmetic of integral quadratic forms (1971) (22)
- Topological Problems in Wave Propagation Theory and Topological Economy Principle in Algebraic Geometry (1999) (22)
- Singularity Theory II Classification and Applications (1993) (22)
- Symplectization, Complexification and Mathematical Trinities (1999) (21)
- Number-Theoretical Turbulence in Fermat–Euler Arithmetics and Large Young Diagrams Geometry Statistics (2005) (21)
- On the topology of three-dimensional steady flows of an ideal fluid (1966) (21)
- First Steps of Local Symplectic Algebra (1999) (20)
- Geometry and Growth Rate of Frobenius Numbers of Additive Semigroups (2006) (19)
- Singularities in variational calculus (1984) (19)
- The Vassiliev Theory of Discriminants and Knots (1994) (19)
- The stability problem and ergodic properties for classical dynamical systems (1968) (19)
- Critical Points of Functions (1998) (19)
- Classification of bimodal critical points of functions (1974) (19)
- Optimization in Mean and Phase Transitions in Controlled Dynamical Systems (2002) (19)
- Smooth functions statistics (2006) (18)
- BIFURCATIONS AND SINGULARITIES IN MATHEMATICS AND MECHANICS (1989) (18)
- Complexity of finite sequences of zeros and ones and geometry of finite spaces of functions (2006) (18)
- On the interior scattering of waves, defined by hyperbolic variational principles (1988) (17)
- Algebraic unsolvability of the problem of Lyapunov stability and the problem of topological classification of singular points of an analytic system of differential equations (1971) (17)
- Topological classification of real trigonometric polynomials and cyclic serpents polyhedron (1997) (17)
- The Topology of Algebra: Combinatorics of Squaring (2003) (17)
- A Catastrophe Machine (1984) (17)
- Fermat–Euler Dynamical Systems and the Statistics of Arithmetics of Geometric Progressions (2003) (17)
- Dynamics of Intersections (1990) (17)
- Arithmetical Turbulence of Selfsimilar Fluctuations Statistics of Large Frobenius Numbers of Additive Semigroups of Integers (2007) (17)
- Orbits' statistics in chaotic dynamical systems (2008) (16)
- First Steps of Local Contact Algebra (1999) (16)
- The Geometry of A-graded Algebras (1994) (16)
- Dynamical Systems VII: Integrable Systems Nonholonomic Dynamical Systems (1994) (16)
- Lobachevsky triangle altitudes theorem as the Jacobi identity in the Lie algebra of quadratic forms on symplectic plane (2005) (16)
- Ergodic and arithmetical properties of geometrical progression's dynamics and of its orbits (2005) (16)
- SPACES OF LOCALLY CONVEX CURVES IN S AND COMBINATORICS OF THE GROUP B (2012) (15)
- Topological content of the Maxwell theorem on multiple representation of spherical functions (1996) (15)
- Dynamics, Statistics and Projective Geometry of Galois Fields (2010) (15)
- Topology and statistics of formulae of arithmetics (2003) (15)
- Bifurcations of caustics and wave fronts (2012) (15)
- Sur quelques problèmes de la théorie des systèmes dynamiques (1994) (14)
- Remarks on the parabolic curves on surfaces and on the higher-dimensional Möbius-sturm theory (1997) (14)
- On the matricial version of Fermat–Euler congruences (2006) (14)
- Fermat Dynamics, Matrix Arithmetics, Finite Circles, and Finite Lobachevsky Planes (2004) (13)
- Topological properties of eigenoscillations in mathematical physics (2011) (13)
- Astroidal geometry of hypocycloids and the Hessian topology of hyperbolic polynomials (2001) (13)
- Remarks on the Extatic Points of Plane Curves (1996) (13)
- Forgotten and neglected theories of Poincaré (2006) (13)
- Stochastic and deterministic characteristics of orbits in chaotically looking dynamical systems (2009) (12)
- The Arnold-Gelfand Mathematical Seminars (2011) (12)
- The complex Lagrangian Grassmannian (2000) (12)
- Some open problems in the theory of singularities (1983) (12)
- Relatives of the Quotient of the Complex Projective Plane by the Complex Conjugation (1999) (11)
- On the representation of functions of several variables as a superposition of functions of a smaller number of variables (2009) (11)
- Newton's principia read 300 years later (1991) (11)
- Mathematical Understanding of Nature: Essays on Amazing Physical Phenomena and Their Understanding by Mathematicians (2014) (10)
- On the problem of realization of a given Gaussian curvature function (1998) (10)
- Local problems of analysis (1970) (10)
- Topological Classification of Morse Functions and Generalisations of Hilbert's 16-th Problem (2009) (10)
- Singularities, Bifurcations, and Catastrophes (1983) (10)
- Geometry of continued fractions associated with Frobenius numbers (2009) (9)
- I.G. Petrovskii, Hilbert's topological problems, and modern mathematics (2002) (9)
- The topology of real algebraic curves (1973) (9)
- Singularities of Legendre varieties, of evolvents and of fronts at an obstacle (1982) (8)
- Continued fractions of square roots of rational numbers and their statistics (2007) (8)
- Contact structure, relaxation oscillations and singular points of implicit differential equations (1988) (8)
- Topological Problems of the Theory of Asymptotic Curves (1999) (7)
- Opinion: Will mathematics survive? report on the zurich congress (1995) (7)
- Empirical study of stochasticity for deterministic chaotical dynamics of geometric progressions of residues (2009) (7)
- On a Variational Problem Connected with Phase Transitions of Means in Controllable Dynamical Systems (2002) (7)
- Surfaces defined by hyperbolic equations (1988) (7)
- Vladimir I. Arnold - Collected Works (2009) (6)
- Dynamics, Statistics and Projective Geometry of Galois Fields: Preface (2010) (6)
- Towards the legendre sturm theory of space curves (1998) (6)
- Braids of algebraic functions and the cohomology of swallowtails (1968) (6)
- Lagrangian mechanics on manifolds (1989) (6)
- Geometry and dynamics of Galois fields (2004) (6)
- IVAN GEORGIEVICH PETROVSKII (on his seventieth birthday) (1971) (6)
- On a characteristic class arising in quantization conditions (1967) (6)
- Ordinary differential equations , by V. I. Arnold. Pp 334. DM 78. 1992. ISBN 3-540-54813-0 (Springer) (1995) (6)
- Singularities of functions, wave fronts, caustics and multidimensional integrals (2012) (6)
- The simplest examples (2012) (6)
- Matrix Fermat theorem, finite circles and finite Lobachevsky plane (2004) (5)
- Topological classification of trigonometric polynomials related to the affine coxeter group $$\tilde A_2 $$ (2007) (5)
- Some Algebro-Geometrical Aspects of the Newton Attraction Theory (1983) (5)
- Topological classification of morse polynomials (2010) (5)
- Singularity Theory: Critical points of functions on a manifold with boundary, the simple Lie groups BK, CK, and F4, and singularities of evolutes (Volume 33, 1978) (1981) (5)
- Steady-state magnetic field in a periodic flow (1982) (5)
- Statistics of the periods of continued fractions for quadratic irrationals (2008) (5)
- On cohomology classes of algebraic functions invariant under Tschirnhausen transformations (1970) (5)
- Mathematics and physics: mother and daughter or sisters? (1999) (4)
- A mathematical trivium (1991) (4)
- Mathematical Models of Catastrophes. Control of Catastrophic Processes (2006) (4)
- Variational Principles and Methods (2006) (4)
- Stationary magnetic field in a periodic flow fluid (1982) (4)
- The matrix Euler-Fermat theorem (2004) (4)
- Frequent Representations (2004) (4)
- Lengths of periods of continued fractions of square roots of integers (2009) (4)
- From superpositions to KAM theory (1937) (3)
- MATHEMATICAL EVENTS IN THE USSR: Ol'ga Arsen'evna Oleinik (on her sixtieth birthday) (1985) (3)
- Exponential scattering of trajectories and its hydrodynamical applications (1984) (3)
- The Double-Layer Potential (2004) (3)
- Mathematics as profession and vocation (2000) (3)
- Singularity Theory: On matrices depending on parameters (Volume 26, 1971) (1981) (3)
- Basic Principles of Classical Mechanics (2006) (3)
- On one-dimensional cohomology of the Lie algebra of divergence-free vector fields and on rotation numbers of dynamic systems (1969) (3)
- The antiscientifical revolution and mathematics (1998) (3)
- Towards the Legendrian Sturm Theory of Space Curves X X X2. the Legendrian Hulls of Curves in Projective Space P N P N P N and Their Fronts (1998) (3)
- Remarks on the stationary phase method and Coxeter numbers (Volume 28, 1973) (1981) (3)
- From superpositions to KAM theory (1937) (3)
- Statistics of Young Diagrams of Cycles of Dynamical Systems for Finite Tori Automorphisms (2006) (3)
- Olga Aleksandrovna Ladyzhenskaya (obituary) (2004) (2)
- Mathematics of Chaos (2010) (2)
- Theory of Small Oscillations (1988) (2)
- Sur les propiétés topologiques des projections langrangiennes en géométrie sympletique des caustiques (1995) (2)
- Complexification of Tetrahedron and Pseudo-Projective Transformations (2001) (2)
- Lagrangian Grassmannian of a Quaternion Hypersymplectic Space (2001) (2)
- A correction to: Wave front evolution and equivariant morse lemma (1977) (2)
- Vladimir Mikhailovich Alekseev (obituary) (1981) (2)
- Seventeen Papers on Analysis (1963) (2)
- Uniform distribution of non-divisible vectors in an integer space (2009) (2)
- Elements of the large-scale structure of the universe. (1981) (2)
- Evolution of a magnetic field under the action of transfer and diffusion (1983) (2)
- Limiting behaviour of large Frobenius numbers (2007) (2)
- Anatolii Moiseevich Vershik (on his sixtieth birthday) (1994) (2)
- A few words on Andrei Nikolaevich Kolmogorov (1988) (2)
- The Global Theory of Singularities (1998) (2)
- Singularity Theory: Normal forms of functions in neighbourhoods of degenerate critical points (Volume 29, 1974) (1981) (2)
- The Longest Curves of Given Degree and the Quasicrystallic Harnack Theorem in Pseudoperiodic Topology (2002) (2)
- Almost sign-preserving trigonometric polynomials (1996) (2)
- Large Scale Distribution of Matter in the Universe (1984) (2)
- Real algebraic geometry (2013) (2)
- Statistics of the period lengths of the continued fractions for the eigenvalues of the integer matrices of order two (2008) (2)
- Singularity Theory: Singularities of smooth mappings (Volume 23, 1968) (1981) (2)
- Spectral sequences for the reduction to normal forms (2012) (2)
- A remark on the ramification of hyperelliptic integrals as functions of parameters (1968) (2)
- A Renormalization Proof of the Kam Theorem for Non-analytic Perturbations (2007) (2)
- Whitney’s Singularity Theory (1984) (2)
- On the topology of eigenfields (2005) (2)
- Problems to the Seminar, 2003-2004 (2004) (2)
- Nikolai Nikolaevich Nekhoroshev (obituary) (2009) (2)
- Investigation of the equations of motion (1978) (1)
- Singularities in Optimization Problems, the Maxima Function (1984) (1)
- Surveys in Modern Mathematics: The principle of topological economy in algebraic geometry (2005) (1)
- The General Theory for One First-Order Equation (Continued) (2004) (1)
- Differential Equations on Surfaces (1988) (1)
- To what extent are arithmetic progressions of fractional parts stochastic (2008) (1)
- Selim Grigor'evich Krein (on his 80th birthday) (1997) (1)
- Algebraic unsolvability of the problem of stability and the problem of the topological classification of the singular points of analytic systems of differential equations (1970) (1)
- Yakov Borisovich Zel'dovich (Obituary) (1988) (1)
- Random and algebraic permutations’ statistics (2009) (1)
- Lyudvig Dmitrievich Faddeev (on his sixtieth birthday) (1995) (1)
- Arnold in his own words (2014) (1)
- On the Riemann curvature of diffeomorphism groups (1965) (1)
- A.N. Kolmogorov and natural science (2004) (1)
- Are quadratic residues random (2010) (1)
- Topology and statistics of arithmetic and algebraic formulae (1)
- Mathematics and Physics (2005) (1)
- A start to the classification of critical points (2012) (1)
- A note on the Weierstrass preparation theorem (1967) (1)
- Singular Points of Vector Fields in the Real and Complex Planes (1988) (1)
- Problems around Polynomials -the Good, the Bad and the Ugly (2015) (1)
- TOPOLOGICAL COMPLEXITY AND SCHWARZ GENUS OF GENERAL REAL POLYNOMIAL EQUATION (2011) (1)
- What is mathematical physics (2004) (1)
- The period map and the intersection form (2012) (1)
- Critical points of smooth functions and their normal forms (Volume 30, 1975) (1981) (1)
- Quasihomogeneous and semiquasihomogeneous singularities (2012) (1)
- Complex Euler’s groups and values of Euler’s function at complex integer Gauss points (2011) (1)
- Elements of the theory of Picard-Lefschetz (2012) (1)
- Surveys in Modern Mathematics: Mysterious mathematical trinities (2005) (1)
- NIKOLAI IVANOVICH MUSKHELISHVILI (on his eightieth birthday) (1972) (1)
- About Vladimir Abramovich Rokhlin (2014) (1)
- Boris Valerianovich Chirikov (on his sixtieth birthday) (1988) (1)
- Collected works || uniform distribution of points on a sphere and some ergodic properties of solutions of linear ordinary differential equations in a complex region (2009) (1)
- A magnetic field in a moving conducting fluid (1981) (1)
- Galina Nikolaevna Tyurina (obituary) (1971) (1)
- First-Order Partial Differential Equations (1988) (1)
- Vladimir Abramovich Rokhlin (obituary) (1986) (1)
- Vyacheslav Alekseevich Oleinikov (obituary) (1990) (1)
- Géométrie asroîdale et topologie des polynômes hyperboliques (2001) (1)
- Sur les Propriétés Topologiques des Projections Lagrangiennesen Géométrie Sympletique des Caustique (1995) (1)
- Convolution of invariants, and period maps (1990) (0)
- The Theory of Oscillations. The Variational Principle (Continued) (2004) (0)
- Euler ’ s groups of powers of prime complex integers (2014) (0)
- Versal families and bifurcations of differential equations (1972) (0)
- Singularities of the Boundary of Attainability (1986) (0)
- Adiabatic study of the distribution of geometric progressions of residues (2010) (0)
- The Theory of Oscillations. The Variational Principle (2004) (0)
- The mixed Hodge structure of an isolated critical point of a holomorphic function (2012) (0)
- Geometry of Conic Sections (2013) (0)
- Singular Points of Differential Equations in Higher Dimensional Complex Phase Space (1988) (0)
- Singularities of wave fronts and the tennis ball theorem (1994) (0)
- Real, symmetric and boundary singularities (2012) (0)
- Integrable Systems and Integration Methods (2006) (0)
- Review: Shlomo Sternberg, Celestial Mechanics. I, II (1972) (0)
- Catastrophe theory (2nd revised and enlarged edition) (1983) (0)
- Dmitrii Evgen'evich Okhotsimskii (obituary) (2006) (0)
- Periods and Young’s diagram of Fermat–Euler’s geometrical progressions of residues (2010) (0)
- Remarks on the behaviour of flow of a three-dimensional perfect fluid in the presence of a small perturbation of the initial velocity field (1972) (0)
- Tensor Invariants of Equations of Dynamics (2006) (0)
- Non-Integrable Systems (2006) (0)
- The proof of the stability theorem (1985) (0)
- Comments on the paper “On a geometric theorem” by Henri Poincaré (1972) (0)
- Complex oscillatory integrals (2012) (0)
- Dmitrii Andreevich Gudkov (obituary) (1992) (0)
- Dmitrii Viktorovich Anosov (on his 60th birthday) (1997) (0)
- ELEMENTARY NOTIONS OF LATTICE TRIGONOMETRY (2008) (0)
- Topologically Necessary Singularities on Moving Wavefronts and Caustics (1999) (0)
- Book-Review - Mathematical Methods of Classical Mechanics (1982) (0)
- Yurii Alekseevich Mitropol'skii (on his 90th birthday) (2007) (0)
- Singularity Theory: Indices of singular points of 1-forms on a manifold with boundary, convolution of invariants of reflection groups and singular projections of smooth surfaces (Volume 34, 1979) (1981) (0)
- Smooth Surfaces and Their Projections (1984) (0)
- The General Theory for One First-Order Equation (2004) (0)
- THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS TOPOLOGICAL CLASSIFICATION OF TRIGONOMETRIC POLYNOMIALS RELATED TO AFFINE COXETER GROUP Ã2 (2006) (0)
- Symmetry Groups and Order Reduction (2006) (0)
- Projections of surfaces, and singularities of apparent contours (1990) (0)
- The classes \( \sum^{I} \) (2012) (0)
- Appendix I.pmd (2003) (0)
- Dmitrii Andreevich Gudkov (on his seventieth birthday) (1989) (0)
- Geometry of Distributions (1994) (0)
- Stability and instability of dynamic systems with many degrees of freedom (1968) (0)
- Singularities of smooth mappings with additional structures : collected papers (1995) (0)
- Stability and infinitesimal stability (2012) (0)
- Properties of Harmonic Functions (2004) (0)
- Singularities, Bifurcations, and Catastrophe Theories (1984) (0)
- Nikolai Nikolaevich Chentsov (obituary) (1993) (0)
- Bifurcations of Equilibrium States (1984) (0)
- On the matricial version of Fermat–Euler congruences (2006) (0)
- Singularities of caustics and Sturm theory (1994) (0)
- The coefficients of series expansions of integrals, the weight and Hodge filtrations and the spectrum of a critical point (2012) (0)
- The local multiplicity of a holomorphic map (2012) (0)
- Mikhail Vasil'evich Fedoryuk (obituary) (1991) (0)
- Loss of Stability of Equilibrium and of Self-Oscillating Modes of Behaviour (1986) (0)
- The Mysticism of Catastrophe Theory (1986) (0)
- Translator’s Preface to J. Milnor’s book ″Morse Theory″ (1965) (0)
- Henri Poincaré: Selected Works in Three Volumes. Vol. I New Methods of Celestial Mechanics - Preface. From the editorial board. Comments (1971) (0)
- Integrals and differential equations (2012) (0)
- Emmanuil El'evich Shnol' (on his 70th birthday) (1999) (0)
- The local algebra of a map and the Weierstrass preparation theorem (2012) (0)
- Singularities of Accessibility Boundaries (1984) (0)
- The topology of the non-singular level set and the variation operator of a singularity (2012) (0)
- Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences: 359 (1784) (2001) (0)
- Problems of By-Passing Obstacles (1984) (0)
- Foundations of Mechanics; Mathematical Methods of Classical Mechanics; and Classical Dynamical Systems (1980) (0)
- Vladimir Mikhailovich Tikhomirov (on his 70th birthday) (2006) (0)
- Viktor Iosifovich Yudovich (obituary) (2007) (0)
- The Physics of Conic Sections and Ellipsoids (2013) (0)
- Lists of singularities (2012) (0)
- Analytic Theory of Differential Equations (1988) (0)
- The Mystics of Catastrophe Theory (1984) (0)
- Caustics, Wave Fronts, and Their Metamorphoses (1984) (0)
- Dynamics, Statistics and Projective Geometry of Galois Fields: Chaos and randomness in Galois field tables (2010) (0)
- Local Bifurcation Theory (1988) (0)
- Mathematical models and control of catastrophic processes (2005) (0)
- The intersection matrices of singularities of functions of two variables (2012) (0)
- The classification of stable germs by genotype (2012) (0)
- Problems to the Seminar: 15 January 2002 (2002) (0)
- Transformation of waves defined by hyperbolic variational principles (1990) (0)
- Symmetry Groups and Reduction (Lowering the Order) (1988) (0)
- Singularities of Stability Boundaries and the Principle of the Fragility of Good Things (1984) (0)
- The organisation and tabulation of Galois fields (2010) (0)
- Applications of Whitney’s Theory (1984) (0)
- On additive semigroups starting parts (2008) (0)
- The Fundamental Solution for the Laplacian. Potentials (2004) (0)
- The school mathematics circle at Moscow State University: harmonic functions (2009) (0)
- Olga Arsenievna Oleinik (on her 70th birthday) (1997) (0)
- The classes Σ I (1985) (0)
- A Problem for School Pupils (2013) (0)
- Dynamics, Statistics and Projective Geometry of Galois Fields: Projective structures generated by a Galois field (2010) (0)
- WIGNER’S ‘UNREASONABLE EFFECTIVENESS OF MATHEMATICS’ AS A PHILOSOPHICAL PROBLEM (2017) (0)
- The determinator of singularities (2012) (0)
- Spherical Functions. Maxwell’s Theorem. The Removable Singularities Theorem (2004) (0)
- The n-Body Problem (1988) (0)
- The Fourier Method (for the Vibrating String) (2004) (0)
- About the Symposium, Foreword, Contents (1999) (0)
- The simplest properties of the integrals (2012) (0)
- Indice d'un point singulier d'un champ de vecteurs, inégalité de Petrovski-Oleinik et structure de Hodge mixte . Fibrés algébriques sur ρ[n] et problèmes d'algèbre linéaire . Faisceaux cohérents su ρ[n] et problèmes d'algèbre linéaire (1978) (0)
- ON THE TOPOLOGY OF COORIENTED WAVE FRONTS IN SPACES OF SMALL DIMENSIONS (2011) (0)
- The quadratic differential of a map (2012) (0)
- Review of further results (2012) (0)
- ’ s Chord Conjecture (1999) (0)
- Topological methods in the physical sciences [Discussion Meeting Issue. Meeting organised by V. I. Arnold, J. W. Bruce, H. K. Moffatt and R. B. Pelz.] (2001) (0)
- Huygens’ Principle in the Theory of Wave Propagation (2004) (0)
- Symplectic and Contact Geometries (1984) (0)
- Applications of the theory of Lagrangian singularities (1990) (0)
- On a variational principle for the steady flows of perfect fluids and its application to problems of non-linear stability (1966) (0)
- Pseudoquaternion Geometry (2002) (0)
- Points critiques des fonctions sur les variétés à bord, groupes de Lie simples B[k], C[k], F[4] et singularités des volutes . Corps de classe et K-théorie algébrique . Surfaces supersingulières de type K3 sur un corps de caractéristique 2 (1978) (0)
- Dynamics, Statistics and Projective Geometry of Galois Fields: Equipartition of geometric progressions along a finite one-dimensional torus (2010) (0)
- Symplectic and Contact Geometry (1986) (0)
- Stability and instability in classical mechanics (2009) (0)
- The mathematics workshop for schools at Moscow State University (2009) (0)
- Gibbs phenomenon for Fourier series on finite sets (2010) (0)
- Boundary-Value Problems for Laplace’s Equation. Theory of Linear Equations and Systems (2004) (0)
- Lagrangian and Legendre topology (1990) (0)
- The classification of quasihomogeneous functions (2012) (0)
- THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS TO WHAT EXTENT ARE STOCHASTIC THE ARITHMETICAL PROGRESSIONS OF THE FRACTIONAL PARTS? (2008) (0)
- The Problem of Bypassing an Obstacle (1986) (0)
- What is a Galois field (2010) (0)
- Monodromy Groups of Critical Points (1998) (0)
- Basic Properties of Maps (1998) (0)
- A mathematical trivium II (1993) (0)
- Errata to V.I. Arnol’d’s paper: “Small denominators. I.” (2009) (0)
- The Vibrating String (d’Alembert’s Method) (2004) (0)
- Discussion of results (2012) (0)
- Elementary integrals and the resolution of singularities of the phase (2012) (0)
- The classification of Lagrangian and Legendrian singularities (2012) (0)
- A magnetic field in a stationary flow with stretching in a Riemannian manifold fluid (1981) (0)
- The singular index, examples (2012) (0)
- GEVREY-SMOOTHNESS OF INVARIANT TORI FOR NEARLY INTEGRABLE SIMPLECTIC MAPPINGS (2017) (0)
- The bifurcation sets and the monodromy group of a singularity (2012) (0)
- Dynamics, Statistics and Projective Geometry of Galois Fields: Cubic field tables (2010) (0)
- Loss of Stability of Equilibrium and the Generation of Auto-Oscillations (1984) (0)
- Asymptotics and Newton polyhedra (2012) (0)
- Perturbation Theory for Integrable Systems (1988) (0)
- THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS SMOOTH FUNCTIONS STATISTICS (2006) (0)
- The intersection forms of boundary singularities and the topology of complete intersections (2012) (0)
- 1 Fermat-Euler statistics and number-theoretic turbulence (0)

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Vladimir Arnold is affiliated with the following schools:

- Utrecht University
- Moscow State University
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