Edit Profile (opens in new tab) Arnol’d, Vladimir Igorevich (b. 1937 d. 2010) Co-Author Distance 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. more...less 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) · Shaw Prize (2008) Documents Indexed: 406 Publications since 1957, including 76 Books 32 Contributions as Editor · 9 Further Contributions Biographic References: 32 Publications Co-Authors: 157 Co-Authors with 107 Joint Publications 4,769 Co-Co-Authors all top 5 Co-Authors 327 single-authored 18 Novikov, Sergeĭ Petrovich 15 Gamkrelidze, Revaz Valerianovich 11 Varchenko, Alexander Nikolaevich 11 Vasil’ev, Viktor Anatol’evich 10 Ilyashenko, Yulij Sergeevich 10 Sinaĭ, Yakov Grigor’evich 9 Givental, Alexander Borisovich 8 Anosov, Dmitriĭ Viktorovich 8 Khesin, Boris A. 8 Kozlov, Valeriĭ Vasil’evich 7 Gel’fand, Israil’ Moiseevich 7 Kolmogorov, Andreĭ Nikolaevich 7 Viro, Oleg Ya. 6 Gusein-Zade, Sabir M. 6 Khovanskiĭ, Askold Georgievich 6 Mishchenko, Evgeniĭ Frolovich 6 Oleĭnik, Ol’ga Arsen’evna 5 Goryunov, Victor V. 5 Lyashko, O. V. 5 Neĭshtadt, Anatoliĭ Iserovich 5 Osipov, Yuriĭ Sergeevich 5 Vershik, Anatoliĭ Moiseevich 4 4 Vishik, Marko Iosifovich 4 Zelikin, Mikhail Il’ich 3 Avez, Andre 3 Kalashnikov, Anatoliĭ Sergeevich 3 Maslov, Viktor Pavlovich 3 Sevryuk, Mikhail Borisovich 3 Sosinskiĭ, Alekseĭ Bronislavovich 3 Tikhomirov, Vladimir Mikhaĭlovich 3 Tsfasman, Michael A. 3 Vladimirov, Vladimir A. 2 Afraimovich, Valentin S. 2 Alekseev, Valeriĭ Borisovich 2 Aleksandrov, Pavel Sergeevich 2 Avets, A. M. 2 Bogolyubov, Nikolaĭ Nikolaevich 2 Bruce, James William 2 Bukhshtaber, Viktor Matveevich 2 Faddeev, Lyudvig Dmitrievich 2 Fuchs, Dmitry Borisovich 2 Gonchar, Andreĭ Aleksandrovich 2 Iooss, Gérard 2 Korkína, E. I. 2 Lando, Sergei K. 2 Lokutsievskij, O. V. 2 Manin, Yuriĭ Ivanovich 2 Moishezon, Boris G. 2 Pogrebys’kyĭ, Ĭosip Benedyktovych 2 Poincaré, Henri 2 Shafarevich, Igor’ Rostislavovich 2 Shilnikov, Leonid Pavlovich 2 Shubin, Mikhail Aleksandrovich 2 Vladimirov, Vasiliĭ Sergeevich 2 Yakobson, M. V. 2 Zel’dovich, Yakov Borisovich 1 Abramov, Aleksandr Mikhailovich 1 Agranovich, Mikhail Semënovich 1 Akim, Èfraim Lazarevich 1 Alekseev, I. S. 1 Alexandrov, Victor A. 1 Aranson, Samuil Khaĭmovich 1 Atiyah, Michael Francis 1 Avellaneda, Marco 1 Aymanns, A. 1 Barabashev, Alexei G. 1 Baravalle, H. V. 1 Baur, Arnold 1 Beletskiĭ, Vladimir Vasil’evich 1 Berezans’kyĭ, Yuriĭ Makarovych 1 Birman, Mikhail Shlëmovich 1 Bolibrukh, Andreĭ Andreevich 1 Bolsinov, Alexey V. 1 Borisenko, Aleksandr Andreevich 1 Borisyuk, Roman M. 1 Borodkin, L. I. 1 Bouslaev, V. C. 1 Brauer, K. G. 1 Breidenbach, Walter 1 Bronshteĭn, Idel Usherovich 1 Chernous’ko, Feliks Leonidovich 1 Chernyi, Gorimir Gorimirovich 1 Christensen, A. W. 1 Dalets’kyĭ, Yuriĭ L’vovych 1 Danilov-Danilyan, V. I. 1 Demidov, Alexandre Sergeevich 1 Demidov, Sergeĭ Sergeevich 1 Denk, Franz 1 Drenckhahn, Friedrich 1 Dücker, Heinrich 1 Egorov, Yuriĭ Vladimirovich 1 Eneev, T. M. 1 Fettweis, Ewald 1 Filippov, Alexey F. 1 Frolov, Konstantin Vasilyevich 1 Galgani, Luigi 1 Garbe, H. 1 Gel’fand, E. M. 1 Giblin, Peter J. ...and 118 more Co-Authors all top 5 Serials 47 Russian Mathematical Surveys 39 Functional Analysis and its Applications 23 Uspekhi Matematicheskikh Nauk [N. S.] 11 Functional Analysis and Other Mathematics 10 Soviet Mathematics. Doklady 10 Encyclopaedia of Mathematical Sciences 8 Moscow Mathematical Journal 8 Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Fundamental’nye Napravleniya 7 Funktsional’nyĭ Analiz i ego Prilozheniya 7 Translations. Series 2. American Mathematical Society 4 Moscow University Mathematics Bulletin 4 Gazette des Mathématiciens 4 Journal of Soviet Mathematics 4 Sibirskiĭ Matematicheskiĭ Zhurnal 4 Topological Methods in Nonlinear Analysis 3 Communications on Pure and Applied Mathematics 3 Selecta Mathematica Sovietica 3 Vestnik Moskovskogo Universiteta. Seriya I. 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Mathematics 1 Journal of Mathematical Sciences (New York) 1 Selecta Mathematica. New Series 1 European Mathematical Society Newsletter 1 Reviews in Mathematics and Mathematical Physics 1 Chaos 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Journal de Mécanique 1 Graduate Texts in Mathematics 1 London Mathematical Society Lecture Note Series 1 Mathematics and Its Applications. Soviet Series 1 Monographies de l’Enseignement Mathématique 1 Progress in Mathematics 1 University Lecture Series 1 SMF Journée Annuelle 1 Enseignement des Mathématiques (Cassini) 1 Unitext 1 Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta Imeni V. A. Steklova 1 Uspekhi Fizicheskikh Nauk 1 Le Sel et le Fer 1 Universitext 1 Translations. Series 2. American Mathematical Society all top 5 Fields 141 Global analysis, analysis on manifolds (58-XX) 119 Dynamical systems and ergodic theory (37-XX) 87 Manifolds and cell complexes (57-XX) 70 History and biography (01-XX) 55 Mechanics of particles and systems (70-XX) 54 General and overarching topics; collections (00-XX) 49 Differential geometry (53-XX) 48 Ordinary differential equations (34-XX) 40 Number theory (11-XX) 35 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) 16 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 Field theory and polynomials (12-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Functions of a complex variable (30-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 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 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) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 333 Publications have been cited 9,545 times in 7,958 Documents Cited by ▼ Year ▼ Mathematical methods of classical mechanics. Translated by K. Vogtman and A. Weinstein. Zbl 0386.70001 Arnold, V. I. 1,082 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. 574 1966 Topological methods in hydrodynamics. Zbl 0902.76001 Arnold, V. I.; Khesin, B. A. 462 1998 Mathematical methods of classical mechanics. Textbook. 3rd ed., rev. and compl. (Математические методы классической механики. Учебное пособие.) Zbl 0692.70003 Arnol’d, V. I. 420 1989 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. 376 1983 Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by E. Khukhro. 3rd revised ed. Zbl 1105.70002 Arnold, Vladimir I.; Kozlov, Valery V.; Neishtadt, Anatoly I. 261 2006 Small denominators and problems of stability of motion in classical and celestial mechanics. Zbl 0135.42701 Arnol’d, V. I. 260 1963 Ergodic problems of classical mechanics. Zbl 0167.22901 Arnol’d, V. I.; Avez, A. 254 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. 238 1997 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. 208 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. 206 1963 Instability of dynamical systems with several degrees of freedom. Zbl 0135.42602 Arnol’d, V. I. 161 1964 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. 154 2012 Small denominators. I: Mappings of the circumference onto itself. Zbl 0152.41905 Arnol’d, V. I. 148 1965 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. 137 1985 On matrices depending on parameters. Zbl 0259.15011 Arnol’d, V. I. 134 1972 Ordinary differential equations. Translated and edited by Richard A. Silverman. Zbl 0296.34001 Arnold, V. I. 116 1973 Wave front evolution and equivariant Morse lemma. Zbl 0343.58003 Arnol’d, V. I. 110 1976 Characteristic class entering in quantization conditions. Zbl 0175.20303 Arnol’d, V. I. 101 1967 Ergodic problems of classical mechanics. Transl. from the French. Reprint. Zbl 0715.70004 Arnold, V. I.; Avez, A. 100 1989 Problèmes ergodiques de la mécanique classique. Zbl 0149.21704 Arnol’d, V. I.; Avez, A. 91 1967 Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields. Zbl 0411.58013 Arnol’d, V. I. 91 1977 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. 90 1988 The cohomology ring of the colored braid group. Zbl 0277.55002 Arnol’d, V. I. 88 1969 Sur la topologie des ecoulements stationnaires des fluides parfaits. Zbl 0145.22203 Arnol’d, V. I. 85 1965 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. 79 1973 Singularities of caustics and wave fronts. Transl. from the Russian. Zbl 0734.53001 Arnol’d, V. I. 76 1990 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. 75 1972 Topological methods in hydrodynamics. Zbl 0743.76019 Arnold, V. I.; Khesin, B. A. 74 1992 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. 73 1988 Mathematical methods of classical mechanics. (Математические методы классической механики.) Zbl 0647.70001 Arnol’d, V. I. 71 1974 Index of a singular point of a vector field, the Petrovskii-Oleinik inequality, and mixed Hodge structures. Zbl 0407.57025 Arnol’d, V. I. 70 1978 Chapitres supplementaires de la théorie des équations différentielles ordinaires. Traduit du russe par Djilali Enbarek. Zbl 0455.34001 Arnold, V. 64 1980 Local normal forms of functions. Zbl 0336.57022 Arnold, V. I. 59 1976 Conditions for nonlinear stability of stationary plane curvilinear flows of an ideal fluid. Zbl 0141.43901 Arnol’d, V. I. 59 1965 On an apriori estimate in the theory of hydrodynamical stability. Zbl 0191.56303 Arnol’d, V. I. 56 1969 Ordinary differential equations. Transl. from the 3rd Russian ed. by Roger Cooke. Zbl 0744.34001 Arnol’d, Vladimir I. 56 1992 Supplementary chapters to the theory of ordinary differential equations. (Dopolnitel’nye glavy teorii obyknovennykh differentsial’nykh uravnenij.) Zbl 0956.34503 Arnol’d, V. I. 55 1978 Small denominators. I: Mapping the circle onto itself. (Kleine Nenner. I: Über Abbildungen der Kreisperipherie auf sich.) Zbl 0135.42603 Arnol’d, V. I. 53 1964 Arnold’s problems. Translated and revised edition of the 2000 Russian original. Zbl 1051.00002 52 2004 Lectures on bifurcations in versal families. Zbl 0264.58005 Arnol’d, V. I. 52 1973 The asymptotic Hopf invariant and its applications. Zbl 0623.57016 Arnol’d, V. I. 51 1986 Ordinary differential equations. Zbl 0659.58012 Arnol’d, V. I.; Il’yashenko, Yu. S. 48 1988 Les méthodes mathématiques de la mécanique classique. Traduit du russe par Djilali Embarek. Zbl 0385.70001 Arnol’d, V. 46 1976 Critical points of smooth functions and their normal forms. Zbl 0343.58001 Arnol’d, V. I. 45 1975 First steps in symplectic topology. Zbl 0649.58010 Arnol’d, V. I. 43 1986 Dynamical systems I. Ordinary differential equations and smooth dynamical systems. Transl. from the Russian. Zbl 0658.00008 41 1988 Sur une propriété topologique des applications globalement canoniques de la mécanique classique. Zbl 0134.42305 Arnol’d, V. I. 39 1965 Remarks on singularities of finite codimension in complex dynamical systems. Zbl 0249.34035 Arnol’d, V. I. 39 1969 Plane curves, their invariants, perestroikas and classifications. Zbl 0864.57027 Arnold, V. I. 38 1994 Modes and quasimodes. Zbl 0251.70012 Arnol’d, V. I. 37 1972 The Sturm theorems and symplectic geometry. Zbl 0606.58017 Arnol’d, V. I. 37 1985 Mathematical aspects of classical and celestial mechanics. Zbl 0674.70003 Arnol’d, V. I.; Kozlov, V. V.; Nejshtadt, A. I. 36 1987 Remarks on the perturbation theory for problems of Mathieu type. Zbl 0541.34035 Arnol’d, V. I. 34 1983 Normal forms of functions in neighbourhoods of degenerate critical points. Zbl 0304.57018 Arnol’d, V. I. 33 1974 Some algebro-geometrical aspects of the Newton attraction theory. Zbl 0569.58018 Arnol’d, V. I. 33 1983 Mathematical aspects of classical and celestial mechanics. Zbl 0612.70002 Arnol’d, V. I.; Kozlov, V. V.; Nejshtadt, A. I. 33 1985 On functions of three variables. Zbl 0090.27101 Arnol’d, V. I. 32 1957 Symplectic geometry. Zbl 0780.58016 Arnol’d, V. I.; Givental’, A. B. 31 1985 Dynamics of complexity of intersections. Zbl 0782.54020 Arnold, V. I. 30 1990 The geometry of spherical curves and the algebra of quaternions. Zbl 0848.58005 Arnol’d, V. I. 29 1995 Statistics of integral convex polygons. Zbl 0447.52011 Arnol’d, V. I. 28 1980 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. 27 1989 Topological classification of Morse functions and generalisations of Hilbert’s 16-th problem. Zbl 1149.57044 Arnold, Vladimir I. 26 2007 Topological invariants of plane curves and caustics. Zbl 0858.57001 Arnol’d, Vladimir Igorevich 26 1994 Catastrophe theory. Transl. from the Russian by R. K. Thomas. Zbl 0517.58003 Arnold, V. I. 25 1984 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. 25 1979 Higher dimensional continued fractions. Zbl 1044.11596 Arnold, V. I. 24 1998 Topological and ergodic properties of closed 1-forms with incommensurable periods. Zbl 0732.58001 Arnol’d, V. I. 24 1991 Remarks on eigenvalues and eigenvectors of Hermitian matrices, Berry phase, adiabatic connections and quantum Hall effect. Zbl 0841.58008 Arnold, V. I. 23 1995 Kolmogorov’s hydrodynamic attractors. Zbl 0726.76045 Arnol’d, V. I. 23 1991 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. 23 1978 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. 22 1998 Topological classification of trigonometric polynomials and combinatorics of graphs with an equal number of vertices and edges. Zbl 0898.32019 Arnold, V. I. 22 1996 Some remarks on flows of line elements and frames. Zbl 0124.14601 Arnol’d, V. I. 21 1961 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. 21 1961 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. 21 1974 Huygens and Barrow, Newton and Hooke. Pioneers in mathematical analysis and catastrophe theory from evolvents to quasicrystals. Transl. from the Russian by Eric J. F. Primrose. Zbl 0721.01001 Arnol’d, V. I. 21 1990 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. 21 1992 Singularity theory. Selected papers. Zbl 0457.58002 Arnold, V. I. 21 1981 The calculus of snakes and the combinatorics of Bernoulli, Euler, and Springer numbers of Coxeter groups. Zbl 0791.05001 Arnol’d, V. I. 21 1992 Mathematical problems in classical physics. Zbl 0806.53078 Arnold, V. I. 21 1994 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. 20 1966 Topological methods in hydrodynamics. 2nd edition. Zbl 1475.76003 Arnold, Vladimir I.; Khesin, Boris A. 20 2021 Newton’s Principia read 300 years later. Zbl 0693.01005 Arnol’d, V. I.; Vasil’ev, V. A. 19 1989 Remarks on the stationary phase method and Coxeter numbers. Zbl 0291.40005 Arnol’d, V. I. 19 1973 Dynamical systems V. Bifurcation theory and catastrophe theory. Transl. from the Russian by N. D. Kazarinoff. Zbl 0791.00009 19 1994 Singularities of smooth mappings. Zbl 0167.21702 Arnol’d, V. I. 18 1968 Weak asymptotics for the numbers of solutions of Diophantine problems. Zbl 1042.11064 Arnol’d, V. I. 17 1999 Cardiac arrythmias and circle mappings. Zbl 0900.92094 Arnold, V. I. 17 1991 Some remarks on symplectic monodromy of Milnor fibrations. Zbl 0970.53043 Arnold, V. I. 17 1995 A-graded algebras and continued fractions. Zbl 0692.16012 Arnol’d, V. I. 17 1989 A branched covering of \(CP^ 2\to S^ 4\), hyperbolicity and projectivity topology. Zbl 0721.57003 Arnol’d, V. I. 17 1988 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. 17 1997 Ordinary differential equations. Textbook. (Obyknovennye differentsial’nye uravneniya. Uchebnoe posobie). 3rd ed., rev. and compl. Zbl 0577.34001 Arnol’d, V. I. 16 1984 Ten problems. Zbl 0729.58002 Arnol’d, V. I. 16 1990 Contact geometry: The geometrical method of Gibb’s thermodynamics. Zbl 0737.53029 Arnold, V. I. 16 1990 Growth of the magnetic field in three-dimensional steady flow of incompressible fluid. Zbl 0528.76112 Arnol’d, V. I.; Korkina, E. I. 15 1983 Singularities of systems of rays. Zbl 0531.58009 Arnol’d, V. I. 15 1983 Variational principle for three-dimensional steady-state flows of an ideal fluid. Zbl 0163.19807 Arnol’d, V. I. 15 1965 Topological methods in hydrodynamics. 2nd edition. Zbl 1475.76003 Arnold, Vladimir I.; Khesin, Boris A. 20 2021 Experimental mathematics. Zbl 1323.00003 Arnold, V. I. 2 2015 Lectures and problems: a gift to young mathematicians. Translated by Dmitry Fuchs and Mark Saul. Zbl 1331.00009 Arnold, V. I. 1 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 Arnold, Vladimir I. 7 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. 4 2014 Real algebraic geometry. Translated from the Russian by Gerald G. Gould and David Kramer. Zbl 1268.14001 Arnold, Vladimir I. 2 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. 208 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. 154 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. 2 2012 Topological properties of eigenoscillations in mathematical physics. Zbl 1229.35220 Arnold, V. I. 5 2011 Dynamics, statistics and projective geometry of Galois fields. Zbl 1219.00001 Arnold, V. I. 2 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 Arnold, Vladimir I. 3 2010 Topological classification of Morse polynomials. Zbl 1214.57026 Arnold, V. I. 3 2010 Geometry of continued fractions associated with Frobenius numbers. Zbl 1201.11009 Arnold, Vladimir I. 4 2009 Lengths of periods of continued fractions of square roots of integers. Zbl 1208.11013 Arnold, Vladimir I. 4 2009 Stochastic and deterministic characteristics of orbits in chaotically looking dynamical systems. Zbl 1211.37007 Arnold, V. I. 4 2009 Permutations. Zbl 1230.05283 Arnold, V. I. 2 2009 Empirical study of stochasticity for deterministic chaotical dynamics of geometric progressions of residues. Zbl 1184.37011 Arnold, Vladimir I. 1 2009 Nikolai Nikolaevich Nekhoroshev (obituary). Zbl 1175.01064 Abramov, A. M.; Arnol’d, V. I.; Bolsinov, A. V.; Varchenko, A. N.; Galgani, L.; Zhilinskii, B. I.; Il’yashenko, Yu. S.; Kozlov, Valerii V.; Neishtadt, Anatolii I.; Piterbarg, Vladimir I.; Khovanskii, Askold G.; Yashchenko, Valerii V. 1 2009 Uniform distribution of non-divisible vectors in an integer space. Zbl 1241.11088 Arnold, V. I. 1 2009 Orbits’ statistics in chaotic dynamical systems. Zbl 1161.37039 Arnold, V. 2 2008 Statistics of the periods of continued fractions for quadratic irrationals. Zbl 1152.11002 Arnol’d, V. I. 2 2008 Statistics of the period lengths of the continued fractions for the eigenvalues of the integer matrices of order two. Zbl 1178.15018 Arnold, Vladimir I. 1 2008 Topological classification of Morse functions and generalisations of Hilbert’s 16-th problem. Zbl 1149.57044 Arnold, Vladimir I. 26 2007 Arithmetical turbulence of selfsimilar fluctuations statistics of large Frobenius numbers of additive semigroups of integers. Zbl 1232.11046 Arnold, V. 6 2007 Continued fractions of square roots of rational numbers and their statistics. Zbl 1147.11036 Arnol’d, V. I. 4 2007 Topological classification of trigonometric polynomials related to the affine Coxeter group \(\widetilde A_2\). Zbl 1196.58004 Arnold, V. I. 2 2007 Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by E. Khukhro. 3rd revised ed. Zbl 1105.70002 Arnold, Vladimir I.; Kozlov, Valery V.; Neishtadt, Anatoly I. 261 2006 Forgotten and neglected theories of Poincaré. Zbl 1165.01013 Arnol’d, V. I. 10 2006 Geometry and growth rate of Frobenius numbers of additive semigroups. Zbl 1141.11020 Arnold, V. I. 10 2006 On the matricial version of Fermat-Euler congruences. Zbl 1168.05003 Arnold, V. I. 10 2006 Smooth functions statistics. Zbl 1154.26018 Arnold, Vladimir I. 9 2006 Complexity of finite sequences of zeros and ones and geometry of finite spaces of functions. Zbl 1196.11033 Arnold, Vladimir I. 8 2006 Statistics of the symmetric group representations as a natural science question on asymptotics of Young diagrams. Zbl 1171.20305 Arnold, Vladimir 2 2006 From Hilbert’s superposition problem to dynamical systems. Zbl 1096.01007 Arnold, V. I. 2 2006 Statistics of Young diagrams of cycles of dynamical systems for finite tori automorphisms. Zbl 1124.05096 Arnold, V. 1 2006 Lobachevsky triangle altitudes theorem as the Jacobi identity in the Lie algebra of quadratic forms on symplectic plane. Zbl 1092.53055 Arnold, V. 9 2005 Number-theoretical turbulence in Fermat-Euler arithmetics and large Young diagrams geometry statistics. Zbl 1134.11344 Arnold, V. 6 2005 Ergodic and arithmetical properties of geometrical progression’s dynamics and of its orbits. Zbl 1089.11004 Arnold, V. 4 2005 On the topology of the eigenfields. Zbl 1134.35300 Arnold, Vladimir I. 3 2005 Mysterious mathematical trinities. Zbl 1125.00300 Arnold, V. I. 1 2005 Arnold’s problems. Translated and revised edition of the 2000 Russian original. Zbl 1051.00002 52 2004 Lectures on partial differential equations. (Vorlesungen über partielle Differentialgleichungen. Übersetzt aus dem Russischen von Tobias Damm.) Zbl 1076.35001 Arnold, V. I. 14 2004 Fermat dynamics, matrix arithmetics, finite circles, and finite Lobachevsky planes. Zbl 1125.11066 Arnold, V. I. 14 2004 Lectures on partial differential equations. Transl. from the Russian by Roger Cooke. Zbl 1076.35002 Arnold, Vladimir I. 4 2004 From Hilbert’s superposition problem to dynamical systems. Zbl 1187.01024 Arnol’d, V. I. 3 2004 The matrix Euler-Fermat theorem. Zbl 1167.11300 Arnol’d, V. I. 3 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. 2 2004 Ol’ga Aleksandrovna Ladyzhenskaya (obituary). Zbl 1062.01503 Arnol’d, V. I.; Birman, M. Sh.; Vershik, A. M.; et al. 2 2004 Geometry and dynamics of Galois fields. Zbl 1148.37301 Arnol’d, V. I. 2 2004 Arithmetics of binary quadratic forms, symmetry of their continued fractions and geometry of their de Sitter world. Zbl 1044.11016 Arnold, V. 11 2003 The topology of algebra: Combinatorics of squaring. Zbl 1040.05015 Arnold, V. I. 10 2003 Aleksej Vasil’evich Pogorelov (obituary). Zbl 1050.01509 Aleksandrov, V. A.; Arnol’d, V. I.; Borisenko, A. A.; et al. 7 2003 Fermat-Euler dynamical systems and the statistics of arithmetics of geometric progressions. Zbl 1038.11006 Arnold, V. I. 7 2003 Topology and statistics of formulas of arithmetic. Zbl 1124.11304 Arnol’d, V. I. 5 2003 Frequent representations. Zbl 1075.20004 Arnold, V. I. 3 2003 Optimization in mean and phase transitions in controlled dynamical systems. Zbl 1057.49003 Arnol’d, V. I. 14 2002 Pseudoquaternion geometry. Zbl 1039.53082 Arnol’d, V. I. 3 2002 Dynamical systems. IV. Symplectic geometry and its applications. Transl. from the Russian by G. Wassermann. 2nd, expanded and revised ed. Zbl 1048.00010 14 2001 Astroidal geometry of hypercycloids and the Hessian topology of hyperbolic polynomials. Zbl 1058.58018 Arnol’d, V. I. 5 2001 Lagrangian Grassmannian of a quaternion hypersymplectic space. Zbl 1034.53081 Arnol’d, V. I. 3 2001 Complexification of tetrahedron and pseudo-projective transformations. Zbl 0999.51001 Arnold, V. I. 1 2001 On teaching mathematics. Zbl 1242.00021 Arnold, Vładimir I. 1 2001 Mathematics: frontiers and perspectives. Zbl 1047.00015 12 2000 The complex Lagrangian Grassmannian. Zbl 0996.53051 Arnold, V. I. 11 2000 Symplectic geometry and topology. Zbl 1021.53053 Arnold, V. I. 8 2000 Polymathematics: is mathematics a single science or a set of arts? Zbl 0980.00004 Arnold, V. I. 7 2000 Arnold’s problems. (Zadachi Arnol’da.) Zbl 1052.00003 Arnol’d, V. I. 6 2000 Dynamical systems. Zbl 0963.37003 Arnold, Vladimir 3 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 Arnold, Vladimir I. 2 2000 From averaging to statistical physics. Zbl 1034.82001 Arnol’d, V. I. 1 2000 Weak asymptotics for the numbers of solutions of Diophantine problems. Zbl 1042.11064 Arnol’d, V. I. 17 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’yashenko, Yu. S.; Shil’nikov, L. P. 13 1999 From Hilbert’s superposition problem to dynamical systems. Zbl 0967.01012 Arnold, V. I. 10 1999 Simple singularities of curves. Zbl 0991.32015 Arnol’d, V. I. 9 1999 Symplectization, complexification and mathematical trinities. Zbl 0948.01012 Arnold, V. I. 9 1999 First steps of local contact algebra. Zbl 1031.53110 Arnold, V. I. 5 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. 4 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. 2 1999 Pseudoperiodic topology. With a preface (ix–xii) by V. I. Arnold. Zbl 0931.00017 2 1999 First step of local symplectic algebra. Zbl 0970.57015 Arnold, V. I. 2 1999 Relatives of the quotient of the complex projective plane by the complex conjugation. Zbl 0963.53023 Arnold, V. I. 2 1999 Topological problems of the theory of asymptotic curves. Zbl 1010.37012 Arnold, V. I. 2 1999 Topological problems in wave propagation theory and topological economy principle in algebraic geometry. Zbl 0946.01011 Arnold, V. I. 1 1999 Topological methods in hydrodynamics. Zbl 0902.76001 Arnold, V. I.; Khesin, B. A. 462 1998 Higher dimensional continued fractions. Zbl 1044.11596 Arnold, V. I. 24 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’ev, V. A. 22 1998 On teaching mathematics. Zbl 1114.00300 Arnold, V. I. 8 1998 On the problem of realization of a given Gaussian curvature function. Zbl 0935.53001 Arnold, Vladimir 4 1998 Three applications of mathematics. (Trois applications des mathématiques.) Zbl 0967.00008 1 1998 Mathematical problems of hydrodynamics and magnetohydrodynamics. (Problèmes mathématiques de l’hydrodynamique et de la magnétohydrodynamique.) Zbl 0999.76003 Arnold, Vladimir 1 1998 Towards the Legendre Sturm theory of space curves. Zbl 0973.53505 Arnold, V. I. 1 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. 238 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’yashenko, Yu. S. 17 1997 Remarks on the parabolic curves on surfaces and on the higher-dimensional Möbius-Sturm theory. Zbl 0973.53504 Arnold, V. I. 7 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’d, V. I. 6 1997 Separated Dirac operators and asymptotically constant linear systems. Zbl 0902.34073 Arnold, V.; Kalf, H.; Schneider, A. 6 1997 Topological classification of real trigonometric polynomials and cyclic serpents polyhedron. Zbl 0904.58007 Arnold, V. 5 1997 Lectures on partial differential equations. Second edition. (Lektsii ob uravneniyakh s chastnymi proizvodnymi.) Zbl 1055.35500 Arnol’d, V. I. 1 1997 The Arnold-Gelfand mathematical seminars. Zbl 0857.00029 1 1997 ...and 233 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 8,545 Authors 42 Llibre, Jaume 35 Markeev, Anatoliĭ Pavlovich 34 Arnol’d, Vladimir Igorevich 34 Marsden, Jerrold Eldon 33 Neĭshtadt, Anatoliĭ Iserovich 31 Broer, Henk W. 31 Holm, Darryl Dallas 28 Khesin, Boris A. 28 Peralta-Salas, Daniel 27 Dobrokhotov, Sergei Yurievich 25 Celletti, Alessandra 25 Wiggins, Stephen R. 23 de León Rodríguez, Manuel 23 Kozlov, Valeriĭ Vasil’evich 21 de la Llave, Rafael 20 Chierchia, Luigi 20 Dullin, Holger R. 20 Preston, Stephen C. 20 Ratiu, Tudor Stefan 19 Cruzeiro, Ana-Bela 19 Guzzo, Massimiliano 19 Han, Maoan 19 Prykarpatsky, Anatoliy Karolevych 19 Tabachnikov, Serge L. 18 Enciso, Alberto 18 Gaeta, Giuseppe 18 Holmes, Philip J. 17 Bruce, James William 17 Davydov, Alekseĭ Aleksandrovich 16 Cao, Daomin 16 Froeschlé, Claude 16 Gay-Balmaz, François 16 Kolev, Boris 16 Mamaev, Ivan Sergeevich 16 Misiołek, Gerard 16 Nazaikinskii, Vladimir E. 15 Bauer, Martin 15 Fiedler, Bernold 15 Haller, George 15 Kalyakin, Leonid Anatol’evich 15 Modin, Klas 14 Borisov, Alekseĭ Vladimirovich 14 Giné, Jaume 14 Janeczko, Stanisław 14 Meiss, James D. 14 Palacián, Jesús F. 14 Takahashi, Masatomo 14 Vidal, Claudio 14 Yanguas, Patricia 14 Yu, Pei 13 Giorgilli, Antonio 13 Hanßmann, Heinz 13 Luo, Shaokai 13 Mezić, Igor 13 Miranda, Eva 13 Shafarevich, Andreĭ Igorevich 13 Shamolin, Maksim Vladimirovich 13 Vasil’ev, Viktor Anatol’evich 13 Yagasaki, Kazuyuki 12 Akhmet’ev, Pëtr Mikhaĭlovich 12 Albeverio, Sergio A. 12 Bolotin, Sergeĭ Vladimirovich 12 Brenier, Yann 12 Colin de Verdière, Yves 12 Ebeling, Wolfgang 12 Esen, Oğul 12 Gusein-Zade, Sabir M. 12 Ishikawa, Goo 12 Kuksin, Sergeĭ B. 12 Lega, Elena 12 Pavelka, Michal 12 Qi, Guoyuan 12 Sevryuk, Mikhail Borisovich 12 Simó, Carles 12 Zhang, Xiang 11 Bardin, Boris Sabirovich 11 Biasco, Luca 11 Bloch, Anthony Michael 11 Bounemoura, Abed Bounemoura 11 Cardin, Franco 11 Delshams, Amadeu 11 Escher, Joachim 11 Ghil, Michael 11 Grmela, Miroslav 11 Izumiya, Shyuichi 11 Kaloshin, Vadim Yu. 11 Karpenkov, Oleg Nikolaevich 11 Kuznetsov, Yuri Alexandrovich 11 Lenells, Jonatan 11 Lerman, Lev 11 Levi, Mark L. 11 Martín de Diego, David 11 Pinzari, Gabriella 11 Sabitov, Kamil’ Basirovich 11 Sidorenko, Vladislav V. 11 Tari, Farid 11 Yau, Stephen Shing-Toung 11 Żołądek, Henryk 10 Aicardi, Francesca 10 Anikin, A. 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