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 4,581 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 Viro, Oleg Ya. 6 Gusein-Zade, Sabir M. 6 Khovanskiĭ, Askold Georgievich 6 Kolmogorov, Andreĭ Nikolaevich 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 B. 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, Ignaz Maria Joseph 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 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 Field theory and polynomials (12-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 328 Publications have been cited 8,407 times in 7,102 Documents Cited by ▼ Year ▼ Mathematical methods of classical mechanics. Translated by K. Vogtman and A. Weinstein. Zbl 0386.70001Arnold, V. I. 1,006 1978 Sur la géométrie différentielle des groupes de Lie de dimension infinite et ses applications à l’hydrodynamique des fluides parfaits. Zbl 0148.45301Arnol’d, V. I. 541 1966 Topological methods in hydrodynamics. Zbl 0902.76001Arnold, V. I.; Khesin, B. A. 426 1998 Geometrical methods in the theory of ordinary differential equations. Transl. from the Russian by Joseph Szuecs, ed. by Mark Levi. Zbl 0507.34003Arnold, V. I. 355 1983 Ergodic problems of classical mechanics. Zbl 0167.22901Arnol’d, V. I.; Avez, A. 245 1968 Small denominators and problems of stability of motion in classical and celestial mechanics. Zbl 0135.42701Arnol’d, V. I. 239 1963 Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by A. Iacob. 2nd printing of the 2nd ed. 1993. Zbl 0885.70001Arnold, V. I.; Kozlov, V. V.; Neishtadt, A. I. 233 1997 Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by E. Khukhro. 3rd revised ed. Zbl 1105.70002Arnold, Vladimir I.; Kozlov, Valery V.; Neishtadt, Anatoly I. 230 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 1290.58001Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N. 199 2012 Proof of a theorem of A. N. Kolmogorov on the invariance of quasi-periodic motions under small perturbations of the Hamiltonian. Zbl 0129.16606Arnol’d, V. I. 177 1963 Instability of dynamical systems with several degrees of freedom. Zbl 0135.42602Arnol’d, V. I. 154 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 1297.32001Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N. 153 2012 Mathematical methods of classical mechanics. Textbook. 3rd ed., rev. and compl. (Математические методы классической механики. Учебное пособие.) Zbl 0692.70003Arnol’d, V. I. 152 1989 Small denominators. I: Mappings of the circumference onto itself. Zbl 0152.41905Arnol’d, V. I. 144 1965 On matrices depending on parameters. Zbl 0259.15011Arnol’d, V. I. 124 1972 Ordinary differential equations. Translated and edited by Richard A. Silverman. Zbl 0296.34001Arnold, V. I. 113 1973 Wave front evolution and equivariant Morse lemma. Zbl 0343.58003Arnol’d, V. I. 107 1976 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 0554.58001Arnol’d, V. I.; Gusejn-Zade, S. M.; Varchenko, A. N. 96 1985 Ergodic problems of classical mechanics. Transl. from the French. Reprint. Zbl 0715.70004Arnold, V. I.; Avez, A. 95 1989 Characteristic class entering in quantization conditions. Zbl 0175.20303Arnol’d, V. I. 90 1967 Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields. Zbl 0411.58013Arnol’d, V. I. 85 1977 Problèmes ergodiques de la mécanique classique. Zbl 0149.21704Arnol’d, V. I.; Avez, A. 85 1967 The cohomology ring of the colored braid group. Zbl 0277.55002Arnol’d, V. I. 81 1969 Sur la topologie des ecoulements stationnaires des fluides parfaits. Zbl 0145.22203Arnol’d, V. I. 79 1965 Topological methods in hydrodynamics. Zbl 0743.76019Arnold, V. I.; Khesin, B. A. 73 1992 Normal forms for functions near degenerate critical points, the Weyl groups of A\(_k\), D\(_k\), E\(_k\) and lagrangian singularities. Zbl 0278.57011Arnol’d, V. I. 67 1973 Index of a singular point of a vector field, the Petrovskii-Oleinik inequality, and mixed Hodge structures. Zbl 0407.57025Arnol’d, V. I. 66 1978 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 0247.47010Maslov, V. P. 63 1972 Chapitres supplementaires de la théorie des équations différentielles ordinaires. Traduit du russe par Djilali Enbarek. Zbl 0455.34001Arnold, V. 62 1980 Mathematical methods of classical mechanics. (Математические методы классической механики.) Zbl 0647.70001Arnol’d, V. I. 60 1974 Singularities of differentiable maps. Volume II: Monodromy and asymptotics of integrals. Transl. from the Russian by Hugh Porteous. Zbl 0659.58002Arnol’d, V. I.; Gusejn-Zade, S. M.; Varchenko, A. N. 58 1988 Local normal forms of functions. Zbl 0336.57022Arnold, V. I. 57 1976 Singularities of caustics and wave fronts. Transl. from the Russian. Zbl 0734.53001Arnol’d, V. I. 57 1990 Conditions for nonlinear stability of stationary plane curvilinear flows of an ideal fluid. Zbl 0141.43901Arnol’d, V. I. 55 1965 Lectures on bifurcations in versal families. Zbl 0264.58005Arnol’d, V. I. 51 1973 On an apriori estimate in the theory of hydrodynamical stability. Zbl 0191.56303Arnol’d, V. I. 50 1969 Supplementary chapters to the theory of ordinary differential equations. (Dopolnitel’nye glavy teorii obyknovennykh differentsial’nykh uravnenij.) Zbl 0956.34503Arnol’d, V. I. 47 1978 Ordinary differential equations. Zbl 0659.58012Arnol’d, V. I.; Il’yashenko, Yu. S. 47 1988 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 0648.34002Arnol’d, V. I. 46 1988 The asymptotic Hopf invariant and its applications. Zbl 0623.57016Arnol’d, V. I. 46 1986 Arnold’s problems. Translated and revised edition of the 2000 Russian original. Zbl 1051.00002 42 2004 Critical points of smooth functions and their normal forms. Zbl 0343.58001Arnol’d, V. I. 42 1975 First steps in symplectic topology. Zbl 0649.58010Arnol’d, V. I. 41 1986 Les méthodes mathématiques de la mécanique classique. Traduit du russe par Djilali Embarek. Zbl 0385.70001Arnol’d, V. 40 1976 Remarks on singularities of finite codimension in complex dynamical systems. Zbl 0249.34035Arnol’d, V. I. 39 1969 Sur une propriété topologique des applications globalement canoniques de la mécanique classique. Zbl 0134.42305Arnol’d, V. I. 38 1965 Plane curves, their invariants, perestroikas and classifications. Zbl 0864.57027Arnold, V. I. 37 1994 Mathematical aspects of classical and celestial mechanics. Zbl 0674.70003Arnol’d, V. I.; Kozlov, V. V.; Nejshtadt, A. I. 36 1987 Modes and quasimodes. Zbl 0251.70012Arnol’d, V. I. 35 1972 The Sturm theorems and symplectic geometry. Zbl 0606.58017Arnol’d, V. I. 34 1985 Mathematical aspects of classical and celestial mechanics. Zbl 0612.70002Arnol’d, V. I.; Kozlov, V. V.; Nejshtadt, A. I. 33 1985 Small denominators. I: Mapping the circle onto itself. (Kleine Nenner. I: Über Abbildungen der Kreisperipherie auf sich.) Zbl 0135.42603Arnol’d, V. I. 33 1964 Some algebro-geometrical aspects of the Newton attraction theory. Zbl 0569.58018Arnol’d, V. I. 32 1983 Remarks on the perturbation theory for problems of Mathieu type. Zbl 0541.34035Arnol’d, V. I. 32 1983 Normal forms of functions in neighbourhoods of degenerate critical points. Zbl 0304.57018Arnol’d, V. I. 32 1974 Dynamical systems I. Ordinary differential equations and smooth dynamical systems. Transl. from the Russian. Zbl 0658.00008 30 1988 Symplectic geometry. Zbl 0780.58016Arnol’d, V. I.; Givental’, A. B. 30 1985 On functions of three variables. Zbl 0090.27101Arnol’d, V. I. 29 1957 Statistics of integral convex polygons. Zbl 0447.52011Arnol’d, V. I. 27 1980 The geometry of spherical curves and the algebra of quaternions. Zbl 0848.58005Arnol’d, V. I. 27 1995 Dynamics of complexity of intersections. Zbl 0782.54020Arnold, V. I. 27 1990 Some unsolved problems in the theory of differential equations and mathematical physics. Zbl 0703.35002Arnol’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. 25 1989 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 0431.58010Arnol’d, V. I. 25 1979 Higher dimensional continued fractions. Zbl 1044.11596Arnold, V. I. 24 1998 Topological and ergodic properties of closed 1-forms with incommensurable periods. Zbl 0732.58001Arnol’d, V. I. 23 1991 Topological classification of Morse functions and generalisations of Hilbert’s 16-th problem. Zbl 1149.57044Arnold, Vladimir I. 23 2007 Kolmogorov’s hydrodynamic attractors. Zbl 0726.76045Arnol’d, V. I. 22 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 0415.58004Arnol’d, V. I. 22 1978 Catastrophe theory. Transl. from the Russian by R. K. Thomas. Zbl 0517.58003Arnold, V. I. 21 1984 Mathematical problems in classical physics. Zbl 0806.53078Arnold, V. I. 21 1994 Topological classification of trigonometric polynomials and combinatorics of graphs with an equal number of vertices and edges. Zbl 0898.32019Arnold, V. I. 21 1996 The stability of the equilibrium position of a Hamiltonian system of ordinary differential equations in the general elliptic case. Zbl 0135.42601Arnol’d, V. I. 21 1961 The calculus of snakes and the combinatorics of Bernoulli, Euler, and Springer numbers of Coxeter groups. Zbl 0791.05001Arnol’d, V. I. 20 1992 Remarks on eigenvalues and eigenvectors of Hermitian matrices, Berry phase, adiabatic connections and quantum Hall effect. Zbl 0841.58008Arnold, V. I. 20 1995 Singularity theory. Selected papers. Zbl 0457.58002Arnold, V. I. 20 1981 Singularity theory I. Transl. from the Russian by A. Iacob. 2nd printing of the 1st ed. 1993. Zbl 0901.58001Arnold, V. I.; Goryunov, V. V.; Lyashko, O. V.; Vasil’ev, V. A. 20 1998 Topological invariants of plane curves and caustics. Zbl 0858.57001Arnol’d, Vladimir Igorevich 19 1994 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 0296.34002Arnold, V. 19 1974 Some remarks on flows of line elements and frames. Zbl 0124.14601Arnol’d, V. I. 19 1961 Ordinary differential equations. Transl. from the 3rd Russian ed. by Roger Cooke. Zbl 0744.34001Arnol’d, Vladimir I. 18 1992 Sur un principe variationnel pour les ecoulements stationnaires des liquides parfaits et ses applications aux problèmes de stabilité non linéaires. Zbl 0161.22903Arnol’d, V. I. 18 1966 Singularities of smooth mappings. Zbl 0167.21702Arnol’d, V. I. 18 1968 Some remarks on symplectic monodromy of Milnor fibrations. Zbl 0970.53043Arnold, V. I. 17 1995 A-graded algebras and continued fractions. Zbl 0692.16012Arnol’d, V. I. 17 1989 Newton’s Principia read 300 years later. Zbl 0693.01005Arnol’d, V. I.; Vasil’ev, V. A. 17 1989 Cardiac arrythmias and circle mappings. Zbl 0900.92094Arnold, V. I. 17 1991 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 0858.34001Anosov, D. V.; Aranson, S. Kh.; Arnold, V. I.; Bronshtein, I. U.; Grines, V. Z.; Il’yashenko, Yu. S. 17 1997 Remarks on the stationary phase method and Coxeter numbers. Zbl 0291.40005Arnol’d, V. I. 17 1973 Weak asymptotics for the numbers of solutions of Diophantine problems. Zbl 1042.11064Arnol’d, V. I. 15 1999 A branched covering of \(CP^ 2\to S^ 4\), hyperbolicity and projectivity topology. Zbl 0721.57003Arnol’d, V. I. 15 1988 Contact geometry: The geometrical method of Gibb’s thermodynamics. Zbl 0737.53029Arnold, V. I. 15 1990 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 0721.01001Arnol’d, V. I. 15 1990 Ordinary differential equations. Textbook. (Obyknovennye differentsial’nye uravneniya. Uchebnoe posobie). 3rd ed., rev. and compl. Zbl 0577.34001Arnol’d, V. I. 14 1984 First steps of symplectic topology. Zbl 0618.58021Arnol’d, V. I. 14 1986 Singularities of systems of rays. Zbl 0531.58009Arnol’d, V. I. 14 1983 Bernoulli-Euler updown numbers associated with function singularities, their combinatorics and arithmetics. Zbl 0755.58015Arnol’d, V. I. 14 1991 Catastrophe theory. Translated from the Russian by G. S. Wassermann. Based on the translation by R. K. Thomas. 3. rev. and exp. ed. Zbl 0746.58001Arnol’d, V. I. 14 1992 Variational principle for three-dimensional steady-state flows of an ideal fluid. Zbl 0163.19807Arnol’d, V. I. 14 1965 Dynamical systems. I: Ordinary differential equations. Zbl 0602.58020Arnol’d, V. I.; Il’yashenko, Yu. S. 13 1985 Optimization in mean and phase transitions in controlled dynamical systems. Zbl 1057.49003Arnol’d, V. I. 13 2002 Topological methods in hydrodynamics. 2nd edition. Zbl 1475.76003Arnold, Vladimir I.; Khesin, Boris A. 11 2021 Experimental mathematics. Zbl 1323.00003Arnold, V. I. 2 2015 Lectures and problems: a gift to young mathematicians. Translated by Dmitry Fuchs and Mark Saul. Zbl 1331.00009Arnold, 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 1354.01038Arnold, Vladimir I. 6 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 1302.00049Arnold, V. I. 4 2014 Real algebraic geometry. Translated from the Russian by Gerald G. Gould and David Kramer. Zbl 1268.14001Arnold, Vladimir I. 1 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 1290.58001Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N. 199 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 1297.32001Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N. 153 2012 Singularities of functions, wave fronts, caustics and multidimensional integrals. Zbl 1255.58002Arnold, V. I.; Varchenko, A. N.; Givental, A. B.; Khovanskii, A. G. 2 2012 Topological properties of eigenoscillations in mathematical physics. Zbl 1229.35220Arnold, V. I. 5 2011 Dynamics, statistics and projective geometry of Galois fields. Zbl 1219.00001Arnold, V. I. 2 2011 Topological classification of Morse polynomials. Zbl 1214.57026Arnold, V. I. 3 2010 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 1187.01033Arnold, Vladimir I. 2 2010 Geometry of continued fractions associated with Frobenius numbers. Zbl 1201.11009Arnold, Vladimir I. 4 2009 Stochastic and deterministic characteristics of orbits in chaotically looking dynamical systems. Zbl 1211.37007Arnold, V. I. 4 2009 Lengths of periods of continued fractions of square roots of integers. Zbl 1208.11013Arnold, Vladimir I. 3 2009 Permutations. Zbl 1230.05283Arnold, V. I. 2 2009 Empirical study of stochasticity for deterministic chaotical dynamics of geometric progressions of residues. Zbl 1184.37011Arnold, Vladimir I. 1 2009 Nikolai Nikolaevich Nekhoroshev (obituary). Zbl 1175.01064Abramov, 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 1241.11088Arnold, V. I. 1 2009 Orbits’ statistics in chaotic dynamical systems. Zbl 1161.37039Arnold, V. 2 2008 Statistics of the periods of continued fractions for quadratic irrationals. Zbl 1152.11002Arnol’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 1178.15018Arnold, Vladimir I. 1 2008 Topological classification of Morse functions and generalisations of Hilbert’s 16-th problem. Zbl 1149.57044Arnold, Vladimir I. 23 2007 Arithmetical turbulence of selfsimilar fluctuations statistics of large Frobenius numbers of additive semigroups of integers. Zbl 1232.11046Arnold, V. 5 2007 Continued fractions of square roots of rational numbers and their statistics. Zbl 1147.11036Arnol’d, V. I. 4 2007 Topological classification of trigonometric polynomials related to the affine Coxeter group \(\widetilde A_2\). Zbl 1196.58004Arnold, V. I. 2 2007 Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by E. Khukhro. 3rd revised ed. Zbl 1105.70002Arnold, Vladimir I.; Kozlov, Valery V.; Neishtadt, Anatoly I. 230 2006 Geometry and growth rate of Frobenius numbers of additive semigroups. Zbl 1141.11020Arnold, V. I. 10 2006 Smooth functions statistics. Zbl 1154.26018Arnold, Vladimir I. 9 2006 On the matricial version of Fermat-Euler congruences. Zbl 1168.05003Arnold, V. I. 9 2006 Forgotten and neglected theories of Poincaré. Zbl 1165.01013Arnol’d, V. I. 9 2006 Complexity of finite sequences of zeros and ones and geometry of finite spaces of functions. Zbl 1196.11033Arnold, Vladimir I. 8 2006 From Hilbert’s superposition problem to dynamical systems. Zbl 1096.01007Arnold, V. I. 2 2006 Statistics of the symmetric group representations as a natural science question on asymptotics of Young diagrams. Zbl 1171.20305Arnold, Vladimir 2 2006 Statistics of Young diagrams of cycles of dynamical systems for finite tori automorphisms. Zbl 1124.05096Arnold, V. 1 2006 Lobachevsky triangle altitudes theorem as the Jacobi identity in the Lie algebra of quadratic forms on symplectic plane. Zbl 1092.53055Arnold, V. 8 2005 Number-theoretical turbulence in Fermat-Euler arithmetics and large Young diagrams geometry statistics. Zbl 1134.11344Arnold, V. 6 2005 Ergodic and arithmetical properties of geometrical progression’s dynamics and of its orbits. Zbl 1089.11004Arnold, V. 4 2005 On the topology of the eigenfields. Zbl 1134.35300Arnold, Vladimir I. 3 2005 Mysterious mathematical trinities. Zbl 1125.00300Arnold, V. I. 1 2005 Arnold’s problems. Translated and revised edition of the 2000 Russian original. Zbl 1051.00002 42 2004 Lectures on partial differential equations. (Vorlesungen über partielle Differentialgleichungen. Übersetzt aus dem Russischen von Tobias Damm.) Zbl 1076.35001Arnold, V. I. 13 2004 Fermat dynamics, matrix arithmetics, finite circles, and finite Lobachevsky planes. Zbl 1125.11066Arnold, V. I. 13 2004 Lectures on partial differential equations. Transl. from the Russian by Roger Cooke. Zbl 1076.35002Arnold, Vladimir 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 1065.12001Alekseev, V. B. 2 2004 Ol’ga Aleksandrovna Ladyzhenskaya (obituary). Zbl 1062.01503Arnol’d, V. I.; Birman, M. Sh.; Vershik, A. M.; et al. 2 2004 From Hilbert’s superposition problem to dynamical systems. Zbl 1187.01024Arnol’d, V. I. 2 2004 The matrix Euler-Fermat theorem. Zbl 1167.11300Arnol’d, V. I. 2 2004 Geometry and dynamics of Galois fields. Zbl 1148.37301Arnol’d, V. I. 2 2004 Arithmetics of binary quadratic forms, symmetry of their continued fractions and geometry of their de Sitter world. Zbl 1044.11016Arnold, V. 10 2003 The topology of algebra: Combinatorics of squaring. Zbl 1040.05015Arnold, V. I. 10 2003 Fermat-Euler dynamical systems and the statistics of arithmetics of geometric progressions. Zbl 1038.11006Arnold, V. I. 7 2003 Aleksej Vasil’evich Pogorelov (obituary). Zbl 1050.01509Aleksandrov, V. A.; Arnol’d, V. I.; Borisenko, A. A.; et al. 6 2003 Topology and statistics of formulas of arithmetic. Zbl 1124.11304Arnol’d, V. I. 4 2003 Frequent representations. Zbl 1075.20004Arnold, V. I. 3 2003 Optimization in mean and phase transitions in controlled dynamical systems. Zbl 1057.49003Arnol’d, V. I. 13 2002 Pseudoquaternion geometry. Zbl 1039.53082Arnol’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 7 2001 Astroidal geometry of hypercycloids and the Hessian topology of hyperbolic polynomials. Zbl 1058.58018Arnol’d, V. I. 5 2001 Lagrangian Grassmannian of a quaternion hypersymplectic space. Zbl 1034.53081Arnol’d, V. I. 2 2001 On teaching mathematics. Zbl 1242.00021Arnold, Vładimir I. 1 2001 Complexification of tetrahedron and pseudo-projective transformations. Zbl 0999.51001Arnold, V. I. 1 2001 Mathematics: frontiers and perspectives. Zbl 1047.00015 10 2000 Symplectic geometry and topology. Zbl 1021.53053Arnold, V. I. 8 2000 The complex Lagrangian Grassmannian. Zbl 0996.53051Arnold, V. I. 7 2000 Polymathematics: is mathematics a single science or a set of arts? Zbl 0980.00004Arnold, V. I. 5 2000 Arnold’s problems. (Zadachi Arnol’da.) Zbl 1052.00003Arnol’d, V. I. 5 2000 Dynamical systems. Zbl 0963.37003Arnold, 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 1080.05501Arnold, Vladimir I. 2 2000 From averaging to statistical physics. Zbl 1034.82001Arnol’d, V. I. 1 2000 Weak asymptotics for the numbers of solutions of Diophantine problems. Zbl 1042.11064Arnol’d, V. I. 15 1999 From Hilbert’s superposition problem to dynamical systems. Zbl 0967.01012Arnold, V. I. 10 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 1038.37500Arnold, V. I.; Afraĭmovich, V. S.; Il’yashenko, Yu. S.; Shil’nikov, L. P. 10 1999 Simple singularities of curves. Zbl 0991.32015Arnol’d, V. I. 9 1999 Symplectization, complexification and mathematical trinities. Zbl 0948.01012Arnold, V. I. 8 1999 First steps of local contact algebra. Zbl 1031.53110Arnold, 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 0974.70003Arnold, V. I.; Avez, A. 3 1999 First step of local symplectic algebra. Zbl 0970.57015Arnold, V. I. 2 1999 Relatives of the quotient of the complex projective plane by the complex conjugation. Zbl 0963.53023Arnold, V. I. 2 1999 Pseudoperiodic topology. With a preface (ix–xii) by V. I. Arnold. Zbl 0931.00017 2 1999 Topological problems of the theory of asymptotic curves. Zbl 1010.37012Arnold, V. I. 2 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 1206.01078Rokhlin, V. A. 1 1999 Topological problems in wave propagation theory and topological economy principle in algebraic geometry. Zbl 0946.01011Arnold, V. I. 1 1999 Topological methods in hydrodynamics. Zbl 0902.76001Arnold, V. I.; Khesin, B. A. 426 1998 Higher dimensional continued fractions. Zbl 1044.11596Arnold, V. I. 24 1998 Singularity theory I. Transl. from the Russian by A. Iacob. 2nd printing of the 1st ed. 1993. Zbl 0901.58001Arnold, V. I.; Goryunov, V. V.; Lyashko, O. V.; Vasil’ev, V. A. 20 1998 On teaching mathematics. Zbl 1114.00300Arnold, V. I. 6 1998 On the problem of realization of a given Gaussian curvature function. Zbl 0935.53001Arnold, Vladimir 4 1998 Three applications of mathematics. (Trois applications des mathématiques.) Zbl 0967.00008 1 1998 Towards the Legendre Sturm theory of space curves. Zbl 0973.53505Arnold, V. I. 1 1998 Mathematical problems of hydrodynamics and magnetohydrodynamics. (Problèmes mathématiques de l’hydrodynamique et de la magnétohydrodynamique.) Zbl 0999.76003Arnold, Vladimir 1 1998 Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by A. Iacob. 2nd printing of the 2nd ed. 1993. Zbl 0885.70001Arnold, V. I.; Kozlov, V. V.; Neishtadt, A. I. 233 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 0858.34001Anosov, 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 0973.53504Arnold, V. I. 7 1997 Separated Dirac operators and asymptotically constant linear systems. Zbl 0902.34073Arnold, V.; Kalf, H.; Schneider, A. 6 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 0923.58010Arnol’d, V. I. 6 1997 Topological classification of real trigonometric polynomials and cyclic serpents polyhedron. Zbl 0904.58007Arnold, V. 5 1997 The Arnold-Gelfand mathematical seminars. Zbl 0857.00029 1 1997 Lectures on partial differential equations. Second edition. (Lektsii ob uravneniyakh s chastnymi proizvodnymi.) Zbl 1055.35500Arnol’d, V. I. 1 1997 ...and 228 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 7,612 Authors 39 Llibre, Jaume 35 Markeev, Anatoliĭ Pavlovich 34 Marsden, Jerrold Eldon 33 Arnol’d, Vladimir Igorevich 31 Broer, Henk W. 31 Holm, Darryl Dallas 31 Neĭshtadt, Anatoliĭ Iserovich 26 Dobrokhotov, Sergei Yurievich 26 Khesin, Boris A. 25 Peralta-Salas, Daniel 25 Wiggins, Stephen R. 24 Celletti, Alessandra 23 Kozlov, Valeriĭ Vasil’evich 20 Dullin, Holger R. 19 Cruzeiro, Ana-Bela 19 Guzzo, Massimiliano 19 Han, Maoan 19 Preston, Stephen C. 19 Ratiu, Tudor Stefan 18 Chierchia, Luigi 18 de la Llave, Rafael 18 Holmes, Philip J. 17 Bruce, James William 17 Davydov, Alekseĭ Aleksandrovich 17 Enciso, Alberto 17 Gaeta, Giuseppe 17 Tabachnikov, Serge L. 16 Froeschlé, Claude 16 Kolev, Boris 16 Misiołek, Gerard 16 Prykarpatsky, Anatoliy Karolevych 15 Bauer, Martin 15 Haller, George 15 Kalyakin, Leonid Anatol’evich 15 Mamaev, Ivan Sergeevich 15 Nazaikinskii, Vladimir E. 14 Borisov, Alekseĭ Vladimirovich 14 Cao, Daomin 14 de León Rodríguez, Manuel 14 Fiedler, Bernold 14 Gay-Balmaz, François 14 Janeczko, Stanisław 14 Meiss, James D. 14 Yu, Pei 13 Hanßmann, Heinz 13 Luo, Shaokai 13 Modin, Klas 13 Palacián, Jesús F. 13 Shafarevich, Andreĭ Igorevich 13 Shamolin, Maksim Vladimirovich 13 Vasil’ev, Viktor Anatol’evich 13 Yanguas, Patricia 12 Albeverio, Sergio A. 12 Brenier, Yann 12 Colin de Verdière, Yves 12 Giné, Jaume 12 Giorgilli, Antonio 12 Gusein-Zade, Sabir M. 12 Lega, Elena 12 Qi, Guoyuan 12 Sevryuk, Mikhail Borisovich 12 Vidal, Claudio 11 Akhmet’ev, Pëtr Mikhaĭlovich 11 Bloch, Anthony Michael 11 Bolotin, Sergeĭ Vladimirovich 11 Cardin, Franco 11 Delshams, Amadeu 11 Ebeling, Wolfgang 11 Escher, Joachim 11 Ghil, Michael 11 Ishikawa, Goo 11 Izumiya, Shyuichi 11 Kaloshin, Vadim Yu. 11 Kuksin, Sergeĭ B. 11 Martín de Diego, David 11 Mezić, Igor 11 Miranda, Eva 11 Sidorenko, Vladislav V. 11 Simó, Carles 11 Zhang, Xiang 10 Aicardi, Francesca 10 Anikin, A. Yu. 10 Bardin, Boris Sabirovich 10 Bounemoura, Abed Bounemoura 10 Gallavotti, Giovanni M. 10 Gelfreich, Vassili 10 Hoveijn, Igor 10 Karpenkov, Oleg Nikolaevich 10 Kirillov, Oleg N. 10 Kuznetsov, Yuri Alexandrovich 10 Lenells, Jonatan 10 Lerman, Lev 10 Levi, Mark L. 10 Pinzari, Gabriella 10 Romero-Fuster, María Carmen 10 Sławianowski, Jan Jerzy 10 Takahashi, Masatomo 10 Tari, Farid 10 Vasil’ev, Alekseĭ Alekseevich 10 Wang, Guodong ...and 7,512 more Authors all top 5 Cited in 646 Serials 390 Physica D 234 Journal of Differential Equations 156 Journal of Mathematical Physics 144 Communications in Mathematical Physics 132 Journal of Geometry and Physics 130 Journal of Applied Mathematics and Mechanics 122 Regular and Chaotic Dynamics 117 Physics Letters. 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