Compute Distance To:
 Author ID: arnold.vladimir-igorevich Published as: Arnol’d, V. I.; Arnold, V. I.; Arnold, Vladimir I.; Arnold, V.; Arnold, Vladimir; Arnol’d, V.; Arnol’d, Vladimir Igorevich; Arnold, Vladimir Igorevich; Arnol’d, Vladimir I.; Arnold, Vładimir I.; Arnold, W. I. Further Spellings: Арнольд Владимир Игоревич Homepage: http://www.pdmi.ras.ru/~arnsem/Arnold/ External Links: MacTutor · MGP · Wikidata · Math-Net.Ru · dblp · GND · IdRef · theses.fr Awards: Wolf Prize (2001)
 Documents Indexed: 405 Publications since 1957, including 75 Books 32 Contributions as Editor · 8 Further Contributions Biographic References: 32 Publications Co-Authors: 154 Co-Authors with 106 Joint Publications 4,424 Co-Co-Authors
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### Fields

 141 Global analysis, analysis on manifolds (58-XX) 116 Dynamical systems and ergodic theory (37-XX) 86 Manifolds and cell complexes (57-XX) 69 History and biography (01-XX) 54 General and overarching topics; collections (00-XX) 49 Differential geometry (53-XX) 48 Mechanics of particles and systems (70-XX) 46 Ordinary differential equations (34-XX) 40 Number theory (11-XX) 34 Algebraic geometry (14-XX) 19 Fluid mechanics (76-XX) 18 Several complex variables and analytic spaces (32-XX) 17 Group theory and generalizations (20-XX) 15 Combinatorics (05-XX) 15 Partial differential equations (35-XX) 8 Real functions (26-XX) 8 Convex and discrete geometry (52-XX) 8 Probability theory and stochastic processes (60-XX) 7 Commutative algebra (13-XX) 6 General topology (54-XX) 6 Algebraic topology (55-XX) 6 Optics, electromagnetic theory (78-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 4 Geometry (51-XX) 4 Quantum theory (81-XX) 4 Statistical mechanics, structure of matter (82-XX) 4 Astronomy and astrophysics (85-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Operator theory (47-XX) 3 Mechanics of deformable solids (74-XX) 3 Systems theory; control (93-XX) 3 Mathematics education (97-XX) 2 Associative rings and algebras (16-XX) 2 Nonassociative rings and algebras (17-XX) 2 Topological groups, Lie groups (22-XX) 2 Functions of a complex variable (30-XX) 2 Special functions (33-XX) 2 Sequences, series, summability (40-XX) 2 Abstract harmonic analysis (43-XX) 2 Functional analysis (46-XX) 2 Relativity and gravitational theory (83-XX) 1 Field theory and polynomials (12-XX) 1 Category theory; homological algebra (18-XX) 1 Measure and integration (28-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Statistics (62-XX) 1 Numerical analysis (65-XX) 1 Computer science (68-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Biology and other natural sciences (92-XX)

### Citations contained in zbMATH Open

312 Publications have been cited 7,337 times in 6,240 Documents Cited by Year
Mathematical methods of classical mechanics. Translated by K. Vogtman and A. Weinstein. Zbl 0386.70001
Arnold, V. I.
1978
Sur la géométrie différentielle des groupes de Lie de dimension infinite et ses applications à l’hydrodynamique des fluides parfaits. Zbl 0148.45301
Arnol’d, V. I.
1966
Topological methods in hydrodynamics. Zbl 0902.76001
Arnold, V. I.; Khesin, B. A.
1998
Geometrical methods in the theory of ordinary differential equations. Transl. from the Russian by Joseph Szuecs, ed. by Mark Levi. Zbl 0507.34003
Arnold, V. I.
1983
Ergodic problems of classical mechanics. Zbl 0167.22901
Arnol’d, V. I.; Avez, A.
1968
Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by A. Iacob. 2nd printing of the 2nd ed. 1993. Zbl 0885.70001
Arnold, V. I.; Kozlov, V. V.; Neishtadt, A. I.
1997
Small denominators and problems of stability of motion in classical and celestial mechanics. Zbl 0135.42701
Arnol’d, V. I.
1963
Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by E. Khukhro. 3rd revised ed. Zbl 1105.70002
2006
Singularities of differentiable maps, Volume 1. Classification of critical points, caustics and wave fronts. Transl. from the Russian by Ian Porteous, edited by V. I. Arnol’d. Reprint of the 1985 hardback edition. Zbl 1290.58001
Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N.
2012
Proof of a theorem of A. N. Kolmogorov on the invariance of quasi-periodic motions under small perturbations of the Hamiltonian. Zbl 0129.16606
Arnol’d, V. I.
1963
Singularities of differentiable maps, Volume 2. Monodromy and asymptotics of integrals. Transl. from the Russian by Hugh Porteous and revised by the authors and James Montaldi. Reprint of the 1988 hardback edition. Zbl 1297.32001
Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N.
2012
Instability of dynamical systems with several degrees of freedom. Zbl 0135.42602
Arnol’d, V. I.
1964
Mathematical methods of classical mechanics. Textbook. 3rd ed., rev. and compl. (Математические методы классической механики. Учебное пособие.) Zbl 0692.70003
Arnol’d, V. I.
1989
Small denominators. I: Mappings of the circumference onto itself. Zbl 0152.41905
Arnol’d, V. I.
1965
On matrices depending on parameters. Zbl 0259.15011
Arnol’d, V. I.
1972
Ordinary differential equations. Translated and edited by Richard A. Silverman. Zbl 0296.34001
Arnold, V. I.
1973
Wave front evolution and equivariant Morse lemma. Zbl 0343.58003
Arnol’d, V. I.
1976
Ergodic problems of classical mechanics. Transl. from the French. Reprint. Zbl 0715.70004
Arnold, V. I.; Avez, A.
1989
Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields. Zbl 0411.58013
Arnol’d, V. I.
1977
Singularities of differentiable maps. Volume I: The classification of critical points, caustics and wave fronts. Transl. from the Russian by Ian Porteous, ed. by V. I. Arnol’d. Zbl 0554.58001
Arnol’d, V. I.; Gusejn-Zade, S. M.; Varchenko, A. N.
1985
Characteristic class entering in quantization conditions. Zbl 0175.20303
Arnol’d, V. I.
1967
Problèmes ergodiques de la mécanique classique. Zbl 0149.21704
Arnol’d, V. I.; Avez, A.
1967
The cohomology ring of the colored braid group. Zbl 0277.55002
Arnol’d, V. I.
1969
Topological methods in hydrodynamics. Zbl 0743.76019
Arnold, V. I.; Khesin, B. A.
1992
Normal forms for functions near degenerate critical points, the Weyl groups of A$$_k$$, D$$_k$$, E$$_k$$ and lagrangian singularities. Zbl 0278.57011
Arnol’d, V. I.
1973
Sur la topologie des ecoulements stationnaires des fluides parfaits. Zbl 0145.22203
Arnol’d, V. I.
1965
Index of a singular point of a vector field, the Petrovskii-Oleinik inequality, and mixed Hodge structures. Zbl 0407.57025
Arnol’d, V. I.
1978
Local normal forms of functions. Zbl 0336.57022
Arnold, V. I.
1976
Théorie des perturbations et méthodes asymptotiques. Suivi de deux notes complementaires de V. I. Arnol’d et V. C. Bouslaev. Traduit par J. Lascoux et R. Seneor. Zbl 0247.47010
Maslov, V. P.
1972
Mathematical methods of classical mechanics. (Математические методы классической механики.) Zbl 0647.70001
Arnol’d, V. I.
1974
Chapitres supplementaires de la théorie des équations différentielles ordinaires. Traduit du russe par Djilali Enbarek. Zbl 0455.34001
Arnold, V.
1980
Singularities of differentiable maps. Volume II: Monodromy and asymptotics of integrals. Transl. from the Russian by Hugh Porteous. Zbl 0659.58002
Arnol’d, V. I.; Gusejn-Zade, S. M.; Varchenko, A. N.
1988
Lectures on bifurcations in versal families. Zbl 0264.58005
Arnol’d, V. I.
1973
Conditions for nonlinear stability of stationary plane curvilinear flows of an ideal fluid. Zbl 0141.43901
Arnol’d, V. I.
1965
On an apriori estimate in the theory of hydrodynamical stability. Zbl 0191.56303
Arnol’d, V. I.
1969
Ordinary differential equations. Zbl 0659.58012
Arnol’d, V. I.; Il’yashenko, Yu. S.
1988
Supplementary chapters to the theory of ordinary differential equations. (Dopolnitel’nye glavy teorii obyknovennykh differentsial’nykh uravnenij.) Zbl 0956.34503
Arnol’d, V. I.
1978
Singularities of caustics and wave fronts. Transl. from the Russian. Zbl 0734.53001
Arnol’d, V. I.
1990
Geometrical methods in the theory of ordinary differntial equations. Transl. from the Russian by Joseph Szücs. Engl. Transl. ed. by Mark Levi. 2nd ed. Zbl 0648.34002
Arnol’d, V. I.
1988
Remarks on singularities of finite codimension in complex dynamical systems. Zbl 0249.34035
Arnol’d, V. I.
1969
The asymptotic Hopf invariant and its applications. Zbl 0623.57016
Arnol’d, V. I.
1986
Arnold’s problems. Translated and revised edition of the 2000 Russian original. Zbl 1051.00002
2004
Critical points of smooth functions and their normal forms. Zbl 0343.58001
Arnol’d, V. I.
1975
Mathematical aspects of classical and celestial mechanics. Zbl 0674.70003
Arnol’d, V. I.; Kozlov, V. V.; Nejshtadt, A. I.
1987
First steps in symplectic topology. Zbl 0649.58010
Arnol’d, V. I.
1986
Plane curves, their invariants, perestroikas and classifications. Zbl 0864.57027
Arnold, V. I.
1994
Mathematical aspects of classical and celestial mechanics. Zbl 0612.70002
Arnol’d, V. I.; Kozlov, V. V.; Nejshtadt, A. I.
1985
Les méthodes mathématiques de la mécanique classique. Traduit du russe par Djilali Embarek. Zbl 0385.70001
Arnol’d, V.
1976
Some algebro-geometrical aspects of the Newton attraction theory. Zbl 0569.58018
Arnol’d, V. I.
1983
Modes and quasimodes. Zbl 0251.70012
Arnol’d, V. I.
1972
Normal forms of functions in neighbourhoods of degenerate critical points. Zbl 0304.57018
Arnol’d, V. I.
1974
Sur une propriété topologique des applications golbalement canoniques de la mécanique classique. Zbl 0134.42305
Arnol’d, V. I.
1965
Remarks on the perturbation theory for problems of Mathieu type. Zbl 0541.34035
Arnol’d, V. I.
1983
Dynamical systems I. Ordinary differential equations and smooth dynamical systems. Transl. from the Russian. Zbl 0658.00008
1988
The Sturm theorems and symplectic geometry. Zbl 0606.58017
Arnol’d, V. I.
1985
Symplectic geometry. Zbl 0780.58016
Arnol’d, V. I.; Givental’, A. B.
1985
Some unsolved problems in the theory of differential equations and mathematical physics. Zbl 0703.35002
Arnol’d, V. I.; Vishik, M. I.; Il’yashenko, Yu. S.; Kalashnikov, A. S.; Kondrat’ev, V. A.; Kruzhkov, S. N.; Landis, E. M.; Millionshchikov, V. M.; Oleĭnik, O. A.; Filippov, A. F.; Shubin, M. A.
1989
The geometry of spherical curves and the algebra of quaternions. Zbl 0848.58005
Arnol’d, V. I.
1995
Indices of singular points of 1-forms on a manifold with boundary, convolution of invariants of reflection groups, and singular projections of smooth surfaces. Zbl 0431.58010
Arnol’d, V. I.
1979
Topological classification of Morse functions and generalisations of Hilbert’s 16-th problem. Zbl 1149.57044
2007
On functions of three variables. Zbl 0090.27101
Arnol’d, V. I.
1957
Statistics of integral convex polygons. Zbl 0447.52011
Arnol’d, V. I.
1980
Higher dimensional continued fractions. Zbl 1044.11596
Arnold, V. I.
1998
Kolmogorov’s hydrodynamic attractors. Zbl 0726.76045
Arnol’d, V. I.
1991
Dynamics of complexity of intersections. Zbl 0782.54020
Arnold, V. I.
1990
Catastrophe theory. Transl. from the Russian by R. K. Thomas. Zbl 0517.58003
Arnold, V. I.
1984
Remarks on eigenvalues and eigenvectors of Hermitian matrices, Berry phase, adiabatic connections and quantum Hall effect. Zbl 0841.58008
Arnold, V. I.
1995
Critical points of functions on a manifold with boundary, the simple Lie groups $$B_4$$, $$C_k$$, and $$F_4$$ and singularities of evolutes. Zbl 0415.58004
Arnol’d, V. I.
1978
Topological and ergodic properties of closed 1-forms with incommensurable periods. Zbl 0732.58001
Arnol’d, V. I.
1991
Topological classification of trigonometric polynomials and combinatorics of graphs with an equal number of vertices and edges. Zbl 0898.32019
Arnold, V. I.
1996
Singularity theory I. Transl. from the Russian by A. Iacob. 2nd printing of the 1st ed. 1993. Zbl 0901.58001
Arnold, V. I.; Goryunov, V. V.; Lyashko, O. V.; Vasil’ev, V. A.
1998
A-graded algebras and continued fractions. Zbl 0692.16012
Arnol’d, V. I.
1989
Equations différentielles ordinaires. Champs de vecteurs. Groupes à un paramètre. Difféomorphismes. Flots. Systemes linéaires. Stabilites des positions d’équilibre. Théorie des oscillations. Equations différentielles sur les variétés. Traduit du russe par Djilali Embarek. Zbl 0296.34002
Arnold, V.
1974
The stability of the equilibrium position of a Hamiltonian system of ordinary differential equations in the general elliptic case. Zbl 0135.42601
Arnol’d, V. I.
1961
Singularities of smooth mappings. Zbl 0167.21702
Arnol’d, V. I.
1968
Singularity theory. Selected papers. Zbl 0457.58002
Arnold, V. I.
1981
Sur un principe variationnel pour les ecoulements stationnaires des liquides parfaits et ses applications aux problèmes de stabilité non linéaires. Zbl 0161.22903
Arnol’d, V. I.
1966
Mathematical problems in classical physics. Zbl 0806.53078
Arnold, V. I.
1994
A branched covering of $$CP^ 2\to S^ 4$$, hyperbolicity and projectivity topology. Zbl 0721.57003
Arnol’d, V. I.
1988
Remarks on the stationary phase method and Coxeter numbers. Zbl 0291.40005
Arnol’d, V. I.
1973
The calculus of snakes and the combinatorics of Bernoulli, Euler, and Springer numbers of Coxeter groups. Zbl 0791.05001
Arnol’d, V. I.
1992
Cardiac arrythmias and circle mappings. Zbl 0900.92094
Arnold, V. I.
1991
Newton’s Principia read 300 years later. Zbl 0693.01005
Arnol’d, V. I.; Vasil’ev, V. A.
1989
Bernoulli-Euler updown numbers associated with function singularities, their combinatorics and arithmetics. Zbl 0755.58015
Arnol’d, V. I.
1991
Ordinary differential equations. Textbook. (Obyknovennye differentsial’nye uravneniya. Uchebnoe posobie). 3rd ed., rev. and compl. Zbl 0577.34001
Arnol’d, V. I.
1984
Some remarks on flows of line elements and frames. Zbl 0124.14601
Arnol’d, V. I.
1961
Weak asymptotics for the numbers of solutions of Diophantine problems. Zbl 1042.11064
Arnol’d, V. I.
1999
Some remarks on symplectic monodromy of Milnor fibrations. Zbl 0970.53043
Arnold, V. I.
1995
Lectures on partial differential equations. (Vorlesungen über partielle Differentialgleichungen. Übersetzt aus dem Russischen von Tobias Damm.) Zbl 1076.35001
Arnold, V. I.
2004
Singularities of systems of rays. Zbl 0531.58009
Arnol’d, V. I.
1983
Catastrophe theory. Translated from the Russian by G. S. Wassermann. Based on the translation by R. K. Thomas. 3. rev. and exp. ed. Zbl 0746.58001
Arnol’d, V. I.
1992
Variational principle for three-dimensional steady-state flows of an ideal fluid. Zbl 0163.19807
Arnol’d, V. I.
1965
Bifurcation theory. Zbl 0797.58003
Arnol’d, V. I.; Afrajmovich, V. S.; Il’yashenko, Yu. S.; Shil’nikov, L. P.
1986
Catastrophe theory. Zbl 0797.58002
Arnol’d, V. I.
1986
Dynamical systems. I: Ordinary differential equations. Zbl 0602.58020
Arnol’d, V. I.; Il’yashenko, Yu. S.
1985
Contact geometry: The geometrical method of Gibb’s thermodynamics. Zbl 0737.53029
Arnold, V. I.
1990
Ordinary differential equations and smooth dynamical systems. Transl. from the Russian by E. R. Dawson and D. O’Shea. 3rd printing of the 1st ed. 1988. Zbl 0858.34001
Anosov, D. V.; Aranson, S. Kh.; Arnold, V. I.; Bronshtein, I. U.; Grines, V. Z.; Il’yashenko, Yu. S.
1997
Optimization in mean and phase transitions in controlled dynamical systems. Zbl 1057.49003
Arnol’d, V. I.
2002
Fermat dynamics, matrix arithmetics, finite circles, and finite Lobachevsky planes. Zbl 1125.11066
Arnold, V. I.
2004
Topological invariants of plane curves and caustics. Zbl 0858.57001
1994
Topological methods in hydrodynamics. 2nd edition. Zbl 1475.76003
Arnold, Vladimir I.; Khesin, Boris A.
2021
Experimental mathematics. Zbl 1323.00003
Arnold, V. I.
2015
Lectures and problems: a gift to young mathematicians. Translated by Dmitry Fuchs and Mark Saul. Zbl 1331.00009
Arnold, V. I.
2015
Vladimir I. Arnold – Collected works. Vol. II. Hydrodynamics, bifurcation theory, and algebraic geometry 1965–1972. Edited by Alexander B. Givental, Boris A. Khesin, Alexander N. Varchenko, Victor A. Vassiliev and Oleg Ya. Viro. Zbl 1354.01038
2014
Mathematical understanding of nature. Essays on amazing physical phenomena and their understanding by mathematicians. Translated from the Russian by Alexei Sossinsky and Olga Sipacheva. Zbl 1302.00049
Arnold, V. I.
2014
Real algebraic geometry. Translated from the Russian by Gerald G. Gould and David Kramer. Zbl 1268.14001
2013
Singularities of differentiable maps, Volume 1. Classification of critical points, caustics and wave fronts. Transl. from the Russian by Ian Porteous, edited by V. I. Arnol’d. Reprint of the 1985 hardback edition. Zbl 1290.58001
Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N.
2012
Singularities of differentiable maps, Volume 2. Monodromy and asymptotics of integrals. Transl. from the Russian by Hugh Porteous and revised by the authors and James Montaldi. Reprint of the 1988 hardback edition. Zbl 1297.32001
Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N.
2012
Singularities of functions, wave fronts, caustics and multidimensional integrals. Zbl 1255.58002
Arnold, V. I.; Varchenko, A. N.; Givental, A. B.; Khovanskii, A. G.
2012
Topological properties of eigenoscillations in mathematical physics. Zbl 1229.35220
Arnold, V. I.
2011
Dynamics, statistics and projective geometry of Galois fields. Zbl 1219.00001
Arnold, V. I.
2011
Vladimir I. Arnold – Collected works. Vol. I. Representations of functions, celestial mechanics, and KAM theory 1957-1965. Edited by Alexander B. Givental, Boris A. Khesin, Jerrold E. Marsden, Alexander N. Varchenko, Victor A. Vissilev, Oleg Ya. Viro and Vladimir M. Zakalyukin. Zbl 1187.01033
2010
Topological classification of Morse polynomials. Zbl 1214.57026
Arnold, V. I.
2010
Geometry of continued fractions associated with Frobenius numbers. Zbl 1201.11009
2009
Stochastic and deterministic characteristics of orbits in chaotically looking dynamical systems. Zbl 1211.37007
Arnold, V. I.
2009
Lengths of periods of continued fractions of square roots of integers. Zbl 1208.11013
2009
Permutations. Zbl 1230.05283
Arnold, V. I.
2009
Empirical study of stochasticity for deterministic chaotical dynamics of geometric progressions of residues. Zbl 1184.37011
2009
Uniform distribution of non-divisible vectors in an integer space. Zbl 1241.11088
Arnold, V. I.
2009
Nikolai Nikolaevich Nekhoroshev (obituary). Zbl 1175.01064
Abramov, A. M.; Arnol&rsquo;d, V. I.; Bolsinov, A. V.; Varchenko, A. N.; Galgani, L.; Zhilinskii, B. I.; Il&rsquo;yashenko, Yu. S.; Kozlov, Valerii V.; Neishtadt, Anatolii I.; Piterbarg, Vladimir I.; Khovanskii, Askold G.; Yashchenko, Valerii V.
2009
Orbits’ statistics in chaotic dynamical systems. Zbl 1161.37039
Arnold, V.
2008
Statistics of the periods of continued fractions for quadratic irrationals. Zbl 1152.11002
Arnol&rsquo;d, V. I.
2008
Statistics of the period lengths of the continued fractions for the eigenvalues of the integer matrices of order two. Zbl 1178.15018
2008
Topological classification of Morse functions and generalisations of Hilbert’s 16-th problem. Zbl 1149.57044
2007
Arithmetical turbulence of selfsimilar fluctuations statistics of large Frobenius numbers of additive semigroups of integers. Zbl 1232.11046
Arnold, V.
2007
Continued fractions of square roots of rational numbers and their statistics. Zbl 1147.11036
Arnol&rsquo;d, V. I.
2007
Topological classification of trigonometric polynomials related to the affine Coxeter group $$\widetilde A_2$$. Zbl 1196.58004
Arnold, V. I.
2007
Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by E. Khukhro. 3rd revised ed. Zbl 1105.70002
2006
Geometry and growth rate of Frobenius numbers of additive semigroups. Zbl 1141.11020
Arnold, V. I.
2006
Forgotten and neglected theories of Poincaré. Zbl 1165.01013
Arnol&rsquo;d, V. I.
2006
Complexity of finite sequences of zeros and ones and geometry of finite spaces of functions. Zbl 1196.11033
2006
Smooth functions statistics. Zbl 1154.26018
2006
On the matricial version of Fermat-Euler congruences. Zbl 1168.05003
Arnold, V. I.
2006
Statistics of the symmetric group representations as a natural science question on asymptotics of Young diagrams. Zbl 1171.20305
2006
From Hilbert’s superposition problem to dynamical systems. Zbl 1096.01007
Arnold, V. I.
2006
Statistics of Young diagrams of cycles of dynamical systems for finite tori automorphisms. Zbl 1124.05096
Arnold, V.
2006
Lobachevsky triangle altitudes theorem as the Jacobi identity in the Lie algebra of quadratic forms on symplectic plane. Zbl 1092.53055
Arnold, V.
2005
Number-theoretical turbulence in Fermat-Euler arithmetics and large Young diagrams geometry statistics. Zbl 1134.11344
Arnold, V.
2005
Ergodic and arithmetical properties of geometrical progression’s dynamics and of its orbits. Zbl 1089.11004
Arnold, V.
2005
On the topology of the eigenfields. Zbl 1134.35300
2005
Arnold’s problems. Translated and revised edition of the 2000 Russian original. Zbl 1051.00002
2004
Lectures on partial differential equations. (Vorlesungen über partielle Differentialgleichungen. Übersetzt aus dem Russischen von Tobias Damm.) Zbl 1076.35001
Arnold, V. I.
2004
Fermat dynamics, matrix arithmetics, finite circles, and finite Lobachevsky planes. Zbl 1125.11066
Arnold, V. I.
2004
Lectures on partial differential equations. Transl. from the Russian by Roger Cooke. Zbl 1076.35002
2004
The matrix Euler-Fermat theorem. Zbl 1167.11300
Arnol&rsquo;d, V. I.
2004
Geometry and dynamics of Galois fields. Zbl 1148.37301
Arnol&rsquo;d, V. I.
2004
Ol’ga Aleksandrovna Ladyzhenskaya (obituary). Zbl 1062.01503
Arnol&rsquo;d, V. I.; Birman, M. Sh.; Vershik, A. M.; et al.
2004
From Hilbert’s superposition problem to dynamical systems. Zbl 1187.01024
Arnol&rsquo;d, V. I.
2004
Abel’s theorem in problems and solutions. Based on the lectures of Professor V. I. Arnold. With a preface and an appendix by Arnold and an appendix by A. Khovanskii. Zbl 1065.12001
Alekseev, V. B.
2004
Arithmetics of binary quadratic forms, symmetry of their continued fractions and geometry of their de Sitter world. Zbl 1044.11016
Arnold, V.
2003
The topology of algebra: Combinatorics of squaring. Zbl 1040.05015
Arnold, V. I.
2003
Fermat-Euler dynamical systems and the statistics of arithmetics of geometric progressions. Zbl 1038.11006
Arnold, V. I.
2003
Aleksej Vasil’evich Pogorelov (obituary). Zbl 1050.01509
Aleksandrov, V. A.; Arnol&rsquo;d, V. I.; Borisenko, A. A.; et al.
2003
Frequent representations. Zbl 1075.20004
Arnold, V. I.
2003
Topology and statistics of formulas of arithmetic. Zbl 1124.11304
Arnol&rsquo;d, V. I.
2003
Optimization in mean and phase transitions in controlled dynamical systems. Zbl 1057.49003
Arnol&rsquo;d, V. I.
2002
Pseudoquaternion geometry. Zbl 1039.53082
Arnol&rsquo;d, V. I.
2002
Astroidal geometry of hypercycloids and the Hessian topology of hyperbolic polynomials. Zbl 1058.58018
Arnol&rsquo;d, V. I.
2001
Dynamical systems. IV. Symplectic geometry and its applications. Transl. from the Russian by G. Wassermann. 2nd, expanded and revised ed. Zbl 1048.00010
2001
Lagrangian Grassmannian of a quaternion hypersymplectic space. Zbl 1034.53081
Arnol&rsquo;d, V. I.
2001
On teaching mathematics. Zbl 1242.00021
2001
Complexification of tetrahedron and pseudo-projective transformations. Zbl 0999.51001
Arnold, V. I.
2001
Mathematics: frontiers and perspectives. Zbl 1047.00015
2000
Symplectic geometry and topology. Zbl 1021.53053
Arnold, V. I.
2000
The complex Lagrangian Grassmannian. Zbl 0996.53051
Arnold, V. I.
2000
Polymathematics: is mathematics a single science or a set of arts? Zbl 0980.00004
Arnold, V. I.
2000
Arnold’s problems. (Zadachi Arnol’da.) Zbl 1052.00003
Arnol&rsquo;d, V. I.
2000
Dynamical systems. Zbl 0963.37003
2000
From averaging to statistical physics. Zbl 1034.82001
Arnol&rsquo;d, V. I.
2000
Euler, Bernoulli and Springer numbers for Coxeter groups and Morse spaces: snake calculus. (Nombres d’Euler, de Bernoulli et de Springer pour les groupes de Coxeter et les espaces de morsification: le calcul des serpents.) Zbl 1080.05501
2000
Weak asymptotics for the numbers of solutions of Diophantine problems. Zbl 1042.11064
Arnol&rsquo;d, V. I.
1999
Bifurcation theory and catastrophe theory. Translated from the 1986 Russian original by N. D. Kazarinoff. Reprint of the original English edition from the series Encyclopaedia of Mathematical Sciences (Dynamical systems V), 5 (1994). Zbl 1038.37500
Arnold, V. I.; Afraĭmovich, V. S.; Il&rsquo;yashenko, Yu. S.; Shil&rsquo;nikov, L. P.
1999
Simple singularities of curves. Zbl 0991.32015
Arnol&rsquo;d, V. I.
1999
From Hilbert’s superposition problem to dynamical systems. Zbl 0967.01012
Arnold, V. I.
1999
Symplectization, complexification and mathematical trinities. Zbl 0948.01012
Arnold, V. I.
1999
First steps of local contact algebra. Zbl 1031.53110
Arnold, V. I.
1999
Ergodic problems of classical mechanics. Transl. from the French and the English by A. V. Borisov, Yu. A. Danilov, A. V. Letchikov, I. S. Mamaev. (Ѐргодические проблемы классической механики.) Zbl 0974.70003
Arnold, V. I.; Avez, A.
1999
First step of local symplectic algebra. Zbl 0970.57015
Arnold, V. I.
1999
Relatives of the quotient of the complex projective plane by the complex conjugation. Zbl 0963.53023
Arnold, V. I.
1999
Pseudoperiodic topology. With a preface (ix–xii) by V. I. Arnold. Zbl 0931.00017
1999
Topological problems of the theory of asymptotic curves. Zbl 1010.37012
Arnold, V. I.
1999
Selected works. Appendix: Reminiscences of V. A. Rokhlin by V. I. Arnol’d, A. M. Vershik, S. P. Novikov and Ya. G. Sinaĭ. With commentaries on Rokhlin’s work by N. Yu. Netsvetaev and Vershik. Edited and with a preface by Vershik. (Избранные работы. Воспоминания о В. А. Рохлине.) Zbl 1206.01078
Rokhlin, V. A.
1999
Topological problems in wave propagation theory and topological economy principle in algebraic geometry. Zbl 0946.01011
Arnold, V. I.
1999
Topological methods in hydrodynamics. Zbl 0902.76001
Arnold, V. I.; Khesin, B. A.
1998
Higher dimensional continued fractions. Zbl 1044.11596
Arnold, V. I.
1998
Singularity theory I. Transl. from the Russian by A. Iacob. 2nd printing of the 1st ed. 1993. Zbl 0901.58001
Arnold, V. I.; Goryunov, V. V.; Lyashko, O. V.; Vasil&rsquo;ev, V. A.
1998
On teaching mathematics. Zbl 1114.00300
Arnold, V. I.
1998
On the problem of realization of a given Gaussian curvature function. Zbl 0935.53001
1998
Towards the Legendre Sturm theory of space curves. Zbl 0973.53505
Arnold, V. I.
1998
Mathematical problems of hydrodynamics and magnetohydrodynamics. (Problèmes mathématiques de l’hydrodynamique et de la magnétohydrodynamique.) Zbl 0999.76003
1998
Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by A. Iacob. 2nd printing of the 2nd ed. 1993. Zbl 0885.70001
Arnold, V. I.; Kozlov, V. V.; Neishtadt, A. I.
1997
Ordinary differential equations and smooth dynamical systems. Transl. from the Russian by E. R. Dawson and D. O’Shea. 3rd printing of the 1st ed. 1988. Zbl 0858.34001
Anosov, D. V.; Aranson, S. Kh.; Arnold, V. I.; Bronshtein, I. U.; Grines, V. Z.; Il&rsquo;yashenko, Yu. S.
1997
Remarks on the parabolic curves on surfaces and on the higher-dimensional Möbius-Sturm theory. Zbl 0973.53504
Arnold, V. I.
1997
Topological classification of real trigonometric polynomials and cyclic serpents polyhedron. Zbl 0904.58007
Arnold, V.
1997
Separated Dirac operators and asymptotically constant linear systems. Zbl 0902.34073
Arnold, V.; Kalf, H.; Schneider, A.
1997
Remarks concerning the Morse theory of a divergence-free vector field, the averaging method, and the motion of a charged particle in a magnetic field. Zbl 0923.58010
Arnol&rsquo;d, V. I.
1997
The Arnold-Gelfand mathematical seminars. Zbl 0857.00029
1997
Lectures on partial differential equations. Second edition. (Lektsii ob uravneniyakh s chastnymi proizvodnymi.) Zbl 1055.35500
Arnol&rsquo;d, V. I.
1997
Topological classification of trigonometric polynomials and combinatorics of graphs with an equal number of vertices and edges. Zbl 0898.32019
Arnold, V. I.
1996
On the number of flattening points on space curves. Zbl 0973.53502
Arnold, V.
1996
...and 212 more Documents
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### Cited in 591 Serials

 355 Physica D 213 Journal of Differential Equations 141 Journal of Mathematical Physics 135 Communications in Mathematical Physics 129 Journal of Applied Mathematics and Mechanics 116 Journal of Geometry and Physics 113 Functional Analysis and its Applications 108 Physics Letters. A 107 Regular and Chaotic Dynamics 90 Chaos, Solitons and Fractals 88 Journal of Mathematical Sciences (New York) 82 Annales de l’Institut Fourier 79 Journal of Mathematical Analysis and Applications 78 Celestial Mechanics and Dynamical Astronomy 70 Archive for Rational Mechanics and Analysis 66 Advances in Mathematics 64 Chaos 62 Proceedings of the Steklov Institute of Mathematics 58 Duke Mathematical Journal 55 Journal of Statistical Physics 54 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 52 Mathematical Notes 52 Reports on Mathematical Physics 49 Inventiones Mathematicae 48 Theoretical and Mathematical Physics 47 Linear Algebra and its Applications 45 Mathematische Annalen 45 Annals of Physics 44 Prikladnaya Matematika i Mekhanika 41 Journal of Fluid Mechanics 41 Transactions of the American Mathematical Society 41 Journal of Nonlinear Science 38 Topology and its Applications 37 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 36 Nonlinearity 35 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 34 Journal of Functional Analysis 33 Ergodic Theory and Dynamical Systems 33 Nonlinear Dynamics 33 Journal of High Energy Physics 32 Annales de l’Institut Henri Poincaré. Physique Théorique 32 Discrete and Continuous Dynamical Systems 31 Applied Mathematics and Computation 31 Compositio Mathematica 31 Journal of Computational and Applied Mathematics 31 Mathematische Zeitschrift 30 Bulletin des Sciences Mathématiques 30 Journal of Nonlinear Mathematical Physics 30 Arnold Mathematical Journal 29 Journal of Soviet Mathematics 29 Differential Geometry and its Applications 29 Communications in Nonlinear Science and Numerical Simulation 28 Mathematical Proceedings of the Cambridge Philosophical Society 28 Nuclear Physics. B 27 Nonlinear Analysis. Theory, Methods & Applications 26 Physica A 26 Systems & Control Letters 26 Journal of Dynamics and Differential Equations 26 Journal of Dynamical and Control Systems 25 Computers & Mathematics with Applications 25 Acta Applicandae Mathematicae 25 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 24 Celestial Mechanics 23 Israel Journal of Mathematics 23 Geometriae Dedicata 23 Russian Journal of Mathematical Physics 23 Comptes Rendus. Mathématique. Académie des Sciences, Paris 23 Functional Analysis and Other Mathematics 23 Journal of Geometric Mechanics 22 Journal of Computational Physics 22 Letters in Mathematical Physics 22 Manuscripta Mathematica 22 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 21 International Journal of Theoretical Physics 21 SIAM Journal on Applied Dynamical Systems 20 ZAMP. Zeitschrift für angewandte Mathematik und Physik 20 Bulletin of the American Mathematical Society. New Series 20 Qualitative Theory of Dynamical Systems 20 Algebraic & Geometric Topology 19 Communications on Pure and Applied Mathematics 19 Proceedings of the American Mathematical Society 19 Journal of Physics A: Mathematical and Theoretical 18 Acta Mechanica 18 Annali di Matematica Pura ed Applicata. Serie Quarta 18 Geometry & Topology 18 Annals of Mathematics. Second Series 17 Physics of Fluids 17 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 17 Indagationes Mathematicae. New Series 17 Acta Mathematica Sinica. English Series 16 General Relativity and Gravitation 16 Journal de Mathématiques Pures et Appliquées. Neuvième Série 16 Doklady Mathematics 16 Differential Equations 15 Computer Methods in Applied Mechanics and Engineering 15 Journal of Algebra 15 Journal of Pure and Applied Algebra 15 Geometric and Functional Analysis. GAFA 15 Communications in Partial Differential Equations 14 Physics Reports ...and 491 more Serials
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### Cited in 63 Fields

 2,187 Dynamical systems and ergodic theory (37-XX) 1,282 Mechanics of particles and systems (70-XX) 924 Partial differential equations (35-XX) 848 Ordinary differential equations (34-XX) 808 Differential geometry (53-XX) 728 Fluid mechanics (76-XX) 679 Global analysis, analysis on manifolds (58-XX) 434 Quantum theory (81-XX) 422 Algebraic geometry (14-XX) 387 Manifolds and cell complexes (57-XX) 312 Several complex variables and analytic spaces (32-XX) 250 Numerical analysis (65-XX) 227 Statistical mechanics, structure of matter (82-XX) 172 Systems theory; control (93-XX) 143 Number theory (11-XX) 139 Probability theory and stochastic processes (60-XX) 138 Relativity and gravitational theory (83-XX) 126 Operator theory (47-XX) 126 Calculus of variations and optimal control; optimization (49-XX) 124 Mechanics of deformable solids (74-XX) 121 Biology and other natural sciences (92-XX) 117 Nonassociative rings and algebras (17-XX) 106 Optics, electromagnetic theory (78-XX) 105 Group theory and generalizations (20-XX) 102 Topological groups, Lie groups (22-XX) 100 Combinatorics (05-XX) 93 Linear and multilinear algebra; matrix theory (15-XX) 87 Algebraic topology (55-XX) 86 Computer science (68-XX) 67 Functional analysis (46-XX) 66 Convex and discrete geometry (52-XX) 57 Functions of a complex variable (30-XX) 55 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 49 Measure and integration (28-XX) 48 Real functions (26-XX) 48 Difference and functional equations (39-XX) 48 Geophysics (86-XX) 45 Commutative algebra (13-XX) 42 Information and communication theory, circuits (94-XX) 40 Harmonic analysis on Euclidean spaces (42-XX) 39 History and biography (01-XX) 39 Astronomy and astrophysics (85-XX) 37 Associative rings and algebras (16-XX) 37 Geometry (51-XX) 34 Operations research, mathematical programming (90-XX) 31 General topology (54-XX) 31 Classical thermodynamics, heat transfer (80-XX) 30 Category theory; homological algebra (18-XX) 30 Approximations and expansions (41-XX) 30 Statistics (62-XX) 24 Special functions (33-XX) 23 General and overarching topics; collections (00-XX) 19 Field theory and polynomials (12-XX) 16 Integral transforms, operational calculus (44-XX) 12 Mathematical logic and foundations (03-XX) 12 Abstract harmonic analysis (43-XX) 9 $$K$$-theory (19-XX) 7 Potential theory (31-XX) 6 Integral equations (45-XX) 5 Order, lattices, ordered algebraic structures (06-XX) 4 Sequences, series, summability (40-XX) 4 Mathematics education (97-XX) 1 General algebraic systems (08-XX)

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