Edit Profile Arnol’d, Vladimir Igorevich Compute Distance To: Compute Author ID: arnold.vladimir-igorevich Published as: Arnol’d, V.; Arnol’d, V. I.; Arnol’d, Vladimir I.; Arnol’d, Vladimir Igorevich; Arnold, V.; Arnold, V. I.; Arnold, Vladimir; Arnold, Vladimir I.; Arnold, Vladimir Igorevich; Arnold, Vładimir I.; Arnold, W. I. Homepage: http://www.pdmi.ras.ru/~arnsem/Arnold/ External Links: MGP · Math-Net.Ru · Wikidata · dblp · GND · MacTutor Awards: Wolf Prize (2001) Documents Indexed: 430 Publications since 1957, including 100 Books Biographic References: 32 Publications all top 5 Co-Authors 334 single-authored 17 Novikov, Sergeĭ Petrovich 14 Gamkrelidze, Revaz Valerianovich 10 Ilyashenko, Yulij Sergeevich 9 Sinaĭ, Yakov Grigor’evich 9 Varchenko, Alexander Nikolaevich 8 Anosov, Dmitriĭ Viktorovich 8 Kozlov, Valeriĭ Vasil’evich 7 Gel’fand, Israil’ Moiseevich 7 Vasil’ev, Viktor Anatol’evich 6 Gusein-Zade, Sabir M. 6 Kolmogorov, Andreĭ Nikolaevich 6 Mishchenko, Evgeniĭ Frolovich 6 Oleĭnik, Ol’ga Arsen’evna 5 Goryunov, Victor V. 5 Khovanskiĭ, Askold Georgievich 5 Lyashko, O. V. 5 Neishtadt, Anatoly Iserovich 5 Osipov, Yuriĭ Sergeevich 4 Avez, Andre 4 Givental, Alexander Borisovich 4 Vershik, Anatoliĭ Moiseevich 4 Vishik, Marko Iosifovich 4 Zelikin, Mikhail Il’ich 3 Kalashnikov, Anatolii S. 3 Sosinskiĭ, Alekseĭ Bronislavovich 3 Tikhomirov, Vladimir Mikhaĭlovich 3 Tsfasman, Michael A. 2 Afraimovich, Valentin S. 2 Aleksandrov, Pavel Sergeevich 2 Avets, A. M. 2 Bukhshtaber, Viktor Matveevich 2 Faddeev, Lyudvig Dmitrievich 2 Fuchs, Dmitry Borisovich 2 Gonchar, Andreĭ Aleksandrovich 2 Khesin, Boris A. 2 Korkína, E. I. 2 Lokutsievskij, O. V. 2 Manin, Yuri Ivanovich 2 Maslov, Viktor Pavlovich 2 Moishezon, Boris G. 2 Shafarevich, Igor’ Rostislavovich 2 Shilnikov, Leonid Pavlovich 2 Shubin, Mikhail Aleksandrovich 2 Viro, Oleg Ya. 2 Vladimirov, Vasiliĭ Sergeevich 2 Vladimirov, Vladimir A. 2 Yakobson, M. V. 2 Zel’dovich, Yakov Borisovich 1 Abramov, A. M. 1 Agranovich, Mikhail Semënovich 1 Akim, Eh. L. 1 Alexandrov, Victor A. 1 Aranson, Samuil Khaĭmovich 1 Atiyah, Michael Francis 1 Avellaneda, Marco 1 Beletsky, 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 Bronshteĭn, Idel Usherovich 1 Bruce, James William 1 Chernousko, E. L. 1 Chernyi, Gorimir Gorimirovich 1 Dalets’kyĭ, Yuriĭ L’vovych 1 Demidov, Alexandre Sergeevich 1 Demidov, Sergeĭ Sergeevich 1 Egorov, Yuriĭ Vladimirovich 1 Ènev, T. M. 1 Filippov, Alexey F. 1 Frolov, Konstantin Vasilyevich 1 Galgani, Luigi 1 Gel’fand, E. M. 1 Glutsyuk, A. M. 1 Gol’denveĭzer, A. L. 1 Gorin, Evgeniĭ Alekseevich 1 Gorodetski, Anton 1 Goryacheva, Irina Georgievna 1 Greuel, Gert-Martin 1 Grines, Vyacheslav Zigmundovich 1 Iooss, Gérard 1 Kaloshin, Vadim Yu. 1 Kator, A. 1 Kazaryan, Maxim Eduardovich 1 Khibnik, Alexander I. 1 Kirillov, Alexandre Aleksandrovich 1 Klimov, Dmitrij M. 1 Kolomogorov, A. N. 1 Kondrat’ev, Vladimir Aleksandrovich 1 Kontsevich, Maxim Lvovich 1 Korchagin, Anatoly B. 1 Kostyuchenko, Anatolii Gordeevich 1 Kruzhkov, Stanislav Nicolayevich 1 Krylov, Alexander L. 1 Kudryavtsev, Lev Dmitrievich 1 Kulish, Petr Petrovich 1 Kutateladze, Semën Samsonovich 1 Landis, Evgenii Mikhailovich ...and 57 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 8 Moscow Mathematical Journal 8 Encyclopaedia of Mathematical Sciences 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. Matematika, Mekhanika 3 Notices of the American Mathematical Society 3 Izvestiya: Mathematics 3 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Paris 3 Proceedings of the Steklov Institute of Mathematics 2 Journal of Applied Mathematics and Mechanics 2 Mathematical Notes 2 Journal of Geometry and Physics 2 Matematicheskiĭ Sbornik. Novaya Seriya 2 Normat 2 Siberian Mathematical Journal 2 Pokroky Matematiky, Fyziky & Astronomie 2 Trudy Seminara Imeni I. G. Petrovskogo 2 St. Petersburg Mathematical Journal 2 Mathematical Physics, Analysis and Geometry 2 Journal of Mathematical Fluid Mechanics 2 Regular and Chaotic Dynamics 2 PMM, Journal of Applied Mathematics and Mechanics 2 Advances in Soviet Mathematics 2 Grundlehren der Mathematischen Wissenschaften 2 Monographs in Mathematics 2 Japanese Journal of Mathematics. 3rd Series 2 MSRI Mathematical Circles Library 2 Modern Birkhäuser Classics 2 Springer-Lehrbuch 1 American Mathematical Monthly 1 Doklady Akademii Nauk SSSR 1 Geophysical and Astrophysical Fluid Dynamics 1 Izvestiya Vysshikh Uchebnykh Zavedeniĭ, Matematika 1 Journal of Mathematical Physics 1 Matematicheskie Zametki 1 Nonlinearity 1 Soviet Scientific Reviews. Section C 1 The Mathematical Intelligencer 1 Annales de l’Institut Fourier 1 Canadian Journal of Mathematics 1 Duke Mathematical Journal 1 Inventiones Mathematicae 1 Istoriko-Matematicheskie Issledovaniya 1 Transactions of the Moscow Mathematical Society 1 Trudy Moskovskogo Matematicheskogo Obshchestva 1 Roczniki Polskiego Towarzystwa Matematycznego. Seria II. Wiadomości Matematyczne 1 Ergodic Theory and Dynamical Systems 1 Physica D 1 Revista Matemática de la Universidad Complutense de Madrid 1 Algebra i Analiz 1 L’Enseignement Mathématique. 2e Série 1 Fiziko-Matematichesko Spisanie 1 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 Soviet Physics. Doklady 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Boletim da Sociedade Brasileira de Matemática. Nova Série 1 Journal of Algebraic Geometry 1 Russian Academy of Sciences. Izvestiya. 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 Applied Mathematical Sciences 1 Graduate Texts in Mathematics 1 London Mathematical Society Lecture Note 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 Universitext 1 Translations. Series 2. American Mathematical Society all top 5 Fields 140 Global analysis, analysis on manifolds (58-XX) 114 Dynamical systems and ergodic theory (37-XX) 84 Manifolds and cell complexes (57-XX) 63 History and biography (01-XX) 50 General and overarching topics; collections (00-XX) 48 Differential geometry (53-XX) 47 Mechanics of particles and systems (70-XX) 43 Ordinary differential equations (34-XX) 40 Number theory (11-XX) 32 Algebraic geometry (14-XX) 17 Group theory and generalizations (20-XX) 17 Several complex variables and analytic spaces (32-XX) 17 Fluid mechanics (76-XX) 15 Combinatorics (05-XX) 14 Partial differential equations (35-XX) 8 Real functions (26-XX) 8 Probability theory and stochastic processes (60-XX) 7 Commutative algebra (13-XX) 7 Convex and discrete geometry (52-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 Statistical mechanics, structure of matter (82-XX) 4 Astronomy and astrophysics (85-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Geometry (51-XX) 3 Mechanics of deformable solids (74-XX) 3 Quantum theory (81-XX) 3 Systems theory; control (93-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) 2 Mathematics education (97-XX) 1 Category theory; homological algebra (18-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Operator theory (47-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 301 Publications have been cited 7,299 times in 6,188 Documents Cited by ▼ Year ▼ Mathematical methods of classical mechanics. Translated by K. Vogtman and A. Weinstein. Zbl 0386.70001Arnold, V. I. 971 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. 414 1966 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. 351 1983 Topological methods in hydrodynamics. Zbl 0902.76001Arnold, V. I.; Khesin, B. A. 344 1998 Ergodic problems of classical mechanics. Zbl 0167.22901Arnol’d, V. I.; Avez, A. 240 1968 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. 214 2012 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. 214 1997 Small denominators and problems of stability of motion in classical and celestial mechanics. Zbl 0135.42701Arnol’d, V. I. 200 1963 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. 175 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. 158 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. 146 1963 Instability of dynamical systems with several degrees of freedom. Zbl 0135.42602Arnol’d, V. I. 124 1964 Ordinary differential equations. Translated and edited by Richard A. Silverman. Zbl 0296.34001Arnold, V. I. 121 1973 Small denominators. I: Mappings of the circumference onto itself. Zbl 0152.41905Arnol’d, V. I. 121 1965 Mathematical methods of classical mechanics. Textbook. 3rd ed., rev. and compl. Zbl 0692.70003Arnol’d, V. I. 114 1989 On matrices depending on parameters. Zbl 0259.15011Arnol’d, V. I. 107 1972 Wave front evolution and equivariant Morse lemma. Zbl 0343.58003Arnol’d, V. I. 97 1976 Ergodic problems of classical mechanics. Transl. from the French. Reprint. Zbl 0715.70004Arnold, V. I.; Avez, A. 83 1989 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. 80 1985 Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields. Zbl 0411.58013Arnol’d, V. I. 75 1977 Problèmes ergodiques de la mécanique classique. Zbl 0149.21704Arnol’d, V. I.; Avez, A. 75 1967 Characteristic class entering in quantization conditions. Zbl 0175.20303Arnol’d, V. I. 73 1967 The cohomology ring of the colored braid group. Zbl 0277.55002Arnol’d, V. I. 66 1969 Index of a singular point of a vector field, the Petrovskii-Oleinik inequality, and mixed Hodge structures. Zbl 0407.57025Arnol’d, V. I. 61 1978 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. 61 1973 Topological methods in hydrodynamics. Zbl 0743.76019Arnold, V. I.; Khesin, B. A. 57 1992 Sur la topologie des ecoulements stationnaires des fluides parfaits. Zbl 0145.22203Arnol’d, V. I. 57 1965 Local normal forms of functions. Zbl 0336.57022Arnold, V. I. 51 1976 Chapitres supplementaires de la théorie des équations différentielles ordinaires. Traduit du russe par Djilali Enbarek. Zbl 0455.34001Arnold, V. 50 1980 Mathematical methods of classical mechanics. Zbl 0647.70001Arnol’d, V. I. 50 1974 Les méthodes mathématiques de la mécanique classique. Traduit du russe par Djilali Embarek. Zbl 0385.70001Arnol’d, V. 48 1976 Lectures on bifurcations in versal families. Zbl 0264.58005Arnol’d, V. I. 48 1973 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. 46 1988 Ordinary differential equations. Zbl 0659.58012Arnol’d, V. I.; Il’yashenko, Yu. S. 45 1988 Mathematical aspects of classical and celestial mechanics. Zbl 0612.70002Arnol’d, V. I.; Kozlov, V. V.; Nejshtadt, A. I. 43 1985 Conditions for nonlinear stability of stationary plane curvilinear flows of an ideal fluid. Zbl 0141.43901Arnol’d, V. I. 43 1965 Dynamical systems I. Ordinary differential equations and smooth dynamical systems. Transl. from the Russian. Zbl 0658.00008Anosov, D. V. (ed.); Arnold, V. I. (ed.); Gamkrelidze, R. V. (ed.) 40 1988 Arnold’s problems. Translated and revised edition of the 2000 Russian original. Zbl 1051.00002Arnold, V. I. (ed.) 39 2004 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. 39 1988 Supplementary chapters to the theory of ordinary differential equations. Zbl 0956.34503Arnol’d, V. I. 39 1978 Remarks on singularities of finite codimension in complex dynamical systems. Zbl 0249.34035Arnol’d, V. I. 39 1969 On an apriori estimate in the theory of hydrodynamical stability. Zbl 0191.56303Arnol’d, V. I. 39 1969 Mathematical aspects of classical and celestial mechanics. Zbl 0674.70003Arnol’d, V. I.; Kozlov, V. V.; Nejshtadt, A. I. 38 1987 Critical points of smooth functions and their normal forms. Zbl 0343.58001Arnol’d, V. I. 35 1975 Plane curves, their invariants, perestroikas and classifications. Zbl 0864.57027Arnold, V. I. 32 1994 Singularities of caustics and wave fronts. Transl. from the Russian. Zbl 0734.53001Arnol’d, V. I. 32 1990 First steps in symplectic topology. Zbl 0649.58010Arnol’d, V. I. 32 1986 The asymptotic Hopf invariant and its applications. Zbl 0623.57016Arnol’d, V. I. 32 1986 Some algebro-geometrical aspects of the Newton attraction theory. Zbl 0569.58018Arnol’d, V. I. 32 1983 Modes and quasimodes. Zbl 0251.70012Arnol’d, V. I. 31 1972 Normal forms of functions in neighbourhoods of degenerate critical points. Zbl 0304.57018Arnol’d, V. I. 30 1974 Remarks on the perturbation theory for problems of Mathieu type. Zbl 0541.34035Arnol’d, V. I. 29 1983 Symplectic geometry. Zbl 0780.58016Arnol’d, V. I.; Givental’, A. B. 27 1985 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. 26 1989 The Sturm theorems and symplectic geometry. Zbl 0606.58017Arnol’d, V. I. 25 1985 Sur une propriété topologique des applications golbalement canoniques de la mécanique classique. Zbl 0134.42305Arnol’d, V. I. 25 1965 The geometry of spherical curves and the algebra of quaternions. Zbl 0848.58005Arnol’d, V. I. 24 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 0431.58010Arnol’d, V. I. 23 1979 Statistics of integral convex polygons. Zbl 0447.52011Arnol’d, V. I. 22 1980 Catastrophe theory. Transl. from the Russian by R. K. Thomas. Zbl 0517.58003Arnold, V. I. 21 1984 Topological classification of Morse functions and generalisations of Hilbert’s 16-th problem. Zbl 1149.57044Arnold, Vladimir I. 20 2007 Higher dimensional continued fractions. Zbl 1044.11596Arnold, V. I. 20 1998 Remarks on eigenvalues and eigenvectors of Hermitian matrices, Berry phase, adiabatic connections and quantum Hall effect. Zbl 0841.58008Arnold, V. I. 19 1995 Singularity theory. Selected papers. Zbl 0457.58002Arnold, V. I. 19 1981 On functions of three variables. Zbl 0090.27101Arnol’d, V. I. 19 1957 Kolmogorov’s hydrodynamic attractors. Zbl 0726.76045Arnol’d, V. I. 18 1991 Dynamics of complexity of intersections. Zbl 0782.54020Arnold, V. I. 18 1990 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. 18 1974 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. 18 1961 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. 17 1998 Topological invariants of plane curves and caustics. Zbl 0858.57001Arnol’d, Vladimir Igorevich 17 1994 Topological and ergodic properties of closed 1-forms with incommensurable periods. Zbl 0732.58001Arnol’d, V. I. 17 1991 A-graded algebras and continued fractions. Zbl 0692.16012Arnol’d, V. I. 17 1989 Supplementary chapters to the theory of ordinary differential equations. Zbl 0956.34501Arnol’d, V. 17 1980 Singularities of smooth mappings. Zbl 0167.21702Arnol’d, V. I. 17 1968 Topological classification of trigonometric polynomials and combinatorics of graphs with an equal number of vertices and edges. Zbl 0898.32019Arnold, V. I. 16 1996 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. 16 1978 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. 16 1966 Lectures on partial differential equations. Zbl 1076.35001Arnold, V. I. 15 2004 Ordinary differential equations. Transl. from the 3rd Russian ed. by Roger Cooke. Zbl 0744.34001Arnol’d, Vladimir I. 15 1992 A branched covering of \(CP^ 2\to S^ 4\), hyperbolicity and projectivity topology. Zbl 0721.57003Arnol’d, V. I. 15 1988 Mathematical problems in classical physics. Zbl 0806.53078Arnold, V. I. 14 1994 Bernoulli-Euler updown numbers associated with function singularities, their combinatorics and arithmetics. Zbl 0755.58015Arnol’d, V. I. 14 1991 Remarks on the stationary phase method and Coxeter numbers. Zbl 0291.40005Arnol’d, V. I. 14 1973 The calculus of snakes and the combinatorics of Bernoulli, Euler, and Springer numbers of Coxeter groups. Zbl 0791.05001Arnol’d, V. I. 13 1992 Cardiac arrythmias and circle mappings. Zbl 0900.92094Arnold, V. I. 13 1991 Newton’s Principia read 300 years later. Zbl 0693.01005Arnol’d, V. I.; Vasil’ev, V. A. 13 1989 Weak asymptotics for the numbers of solutions of Diophantine problems. Zbl 1042.11064Arnol’d, V. I. 12 1999 Some remarks on symplectic monodromy of Milnor fibrations. Zbl 0970.53043Arnold, V. I. 12 1995 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. 12 1992 Ordinary differential equations. Textbook. (Obyknovennye differentsial’nye uravneniya. Uchebnoe posobie). 3rd ed., rev. and compl. Zbl 0577.34001Arnol’d, V. I. 12 1984 Singularities of systems of rays. Zbl 0531.58009Arnol’d, V. I. 12 1983 Some remarks on flows of line elements and frames. Zbl 0124.14601Arnol’d, V. I. 12 1961 The topology of algebra: Combinatorics of squaring. Zbl 1040.05015Arnold, V. I. 11 2003 Catastrophe theory. Zbl 0797.58002Arnol’d, V. I. 11 1986 Bifurcation theory. Zbl 0797.58003Arnol’d, V. I.; Afrajmovich, V. S.; Il’yashenko, Yu. S.; Shil’nikov, L. P. 11 1986 Ordinary differential equations. Transl. and ed. by Richard A. Silverman. 1st paperback ed., 2nd printing. Zbl 0432.34001Arnold, V. I. 11 1980 Variational principle for three-dimensional steady-state flows of an ideal fluid. Zbl 0163.19807Arnol’d, V. I. 11 1965 Arithmetics of binary quadratic forms, symmetry of their continued fractions and geometry of their de Sitter world. Zbl 1044.11016Arnold, V. 10 2003 Optimization in mean and phase transitions in controlled dynamical systems. Zbl 1057.49003Arnol’d, V. I. 10 2002 Experimental mathematics. Zbl 1323.00003Arnold, V. I. 2 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. 4 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. 3 2014 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. 214 2012 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. 158 2012 Singularities of functions, wave fronts, caustics and multidimensional integrals. Zbl 1255.58002Arnold, V. I.; Varchenko, A. N.; Givental, A. B.; Khovanskii, A. G. 1 2012 Topological properties of eigenoscillations in mathematical physics. Zbl 1229.35220Arnold, V. I. 3 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. 2 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. 1 2010 Stochastic and deterministic characteristics of orbits in chaotically looking dynamical systems. Zbl 1211.37007Arnold, V. I. 4 2009 Geometry of continued fractions associated with Frobenius numbers. Zbl 1201.11009Arnold, Vladimir 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 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 Empirical study of stochasticity for deterministic chaotical dynamics of geometric progressions of residues. Zbl 1184.37011Arnold, Vladimir I. 1 2009 Uniform distribution of non-divisible vectors in an integer space. Zbl 1241.11088Arnold, V. I. 1 2009 Statistics of the periods of continued fractions for quadratic irrationals. Zbl 1152.11002Arnol’d, V. I. 2 2008 Orbits’ statistics in chaotic dynamical systems. Zbl 1161.37039Arnold, V. 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. 20 2007 Continued fractions of square roots of rational numbers and their statistics. Zbl 1147.11036Arnol’d, V. I. 4 2007 Arithmetical turbulence of selfsimilar fluctuations statistics of large Frobenius numbers of additive semigroups of integers. Zbl 1232.11046Arnold, V. 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. 175 2006 Complexity of finite sequences of zeros and ones and geometry of finite spaces of functions. Zbl 1196.11033Arnold, Vladimir I. 8 2006 Geometry and growth rate of Frobenius numbers of additive semigroups. Zbl 1141.11020Arnold, V. I. 8 2006 Forgotten and neglected theories of Poincaré. Zbl 1165.01013Arnol’d, V. I. 8 2006 On the matricial version of Fermat-Euler congruences. Zbl 1168.05003Arnold, V. I. 7 2006 Smooth functions statistics. Zbl 1154.26018Arnold, Vladimir I. 7 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 From Hilbert’s superposition problem to dynamical systems. Zbl 1096.01007Arnold, V. I. 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. 2 2005 Arnold’s problems. Translated and revised edition of the 2000 Russian original. Zbl 1051.00002Arnold, V. I. (ed.) 39 2004 Lectures on partial differential equations. Zbl 1076.35001Arnold, V. I. 15 2004 Fermat dynamics, matrix arithmetics, finite circles, and finite Lobachevsky planes. Zbl 1125.11066Arnold, V. I. 9 2004 Lectures on partial differential equations. Transl. from the Russian by Roger Cooke. Zbl 1076.35002Arnold, Vladimir I. 3 2004 Geometry and dynamics of Galois fields. Zbl 1148.37301Arnol’d, V. I. 2 2004 The matrix Euler-Fermat theorem. Zbl 1167.11300Arnol’d, V. I. 2 2004 From Hilbert’s superposition problem to dynamical systems. Zbl 1187.01024Arnol’d, V. I. 1 2004 Ol’ga Aleksandrovna Ladyzhenskaya (obituary). Zbl 1062.01503Arnol’d, V. I.; Birman, M. Sh.; Vershik, A. M.; et al. 1 2004 The topology of algebra: Combinatorics of squaring. Zbl 1040.05015Arnold, V. I. 11 2003 Arithmetics of binary quadratic forms, symmetry of their continued fractions and geometry of their de Sitter world. Zbl 1044.11016Arnold, V. 10 2003 Aleksej Vasil’evich Pogorelov (obituary). Zbl 1050.01509Aleksandrov, V. A.; Arnol’d, V. I.; Borisenko, A. A.; et al. 6 2003 Fermat-Euler dynamical systems and the statistics of arithmetics of geometric progressions. Zbl 1038.11006Arnold, V. I. 6 2003 Topology and statistics of formulas of arithmetic. Zbl 1124.11304Arnol’d, V. I. 3 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. 10 2002 Pseudoquaternion geometry. Zbl 1039.53082Arnol’d, V. I. 3 2002 Astroidal geometry of hypercycloids and the Hessian topology of hyperbolic polynomials. Zbl 1058.58018Arnol’d, V. I. 5 2001 Dynamical systems. IV. Symplectic geometry and its applications. Transl. from the Russian by G. Wassermann. 2nd, expanded and revised ed. Zbl 1048.00010Arnold, V. I. (ed.); Novikov, S. P. (ed.); Gamkrelidze, R. V. (ed.) 4 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 Symplectic geometry and topology. Zbl 1021.53053Arnold, V. I. 9 2000 Mathematics: frontiers and perspectives. Zbl 1047.00015Arnold, V. (ed.); Atiyah, M. (ed.); Lax, P. (ed.); Mazur, B. (ed.) 8 2000 Arnold’s problems. Zbl 1052.00003Arnol’d, V. I. 7 2000 The complex Lagrangian Grassmannian. Zbl 0996.53051Arnold, V. I. 5 2000 Polymathematics: is mathematics a single science or a set of arts? Zbl 0980.00004Arnold, V. I. 4 2000 Dynamical systems. Zbl 0963.37003Arnold, Vladimir 2 2000 From averaging to statistical physics. Zbl 1034.82001Arnol’d, V. I. 1 2000 Singularity theory. Zbl 0971.58022Arnold, Vladimir 1 2000 Weak asymptotics for the numbers of solutions of Diophantine problems. Zbl 1042.11064Arnol’d, V. I. 12 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. 9 1999 Simple singularities of curves. Zbl 0991.32015Arnol’d, V. I. 7 1999 From Hilbert’s superposition problem to dynamical systems. Zbl 0967.01012Arnold, V. I. 7 1999 Symplectization, complexification and mathematical trinities. Zbl 0948.01012Arnold, V. I. 6 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. Zbl 0974.70003Arnold, V. I.; Avez, A. 3 1999 Topological problems of the theory of asymptotic curves. Zbl 1010.37012Arnold, V. I. 2 1999 First step of local symplectic algebra. Zbl 0970.57015Arnold, V. I. 2 1999 Pseudoperiodic topology. With a preface (ix–xii) by V. I. Arnold. Zbl 0931.00017Arnold, V. (ed.); Kontsevich, M. (ed.); Zorich, A. (ed.) 2 1999 Relatives of the quotient of the complex projective plane by the complex conjugation. Zbl 0963.53023Arnold, V. I. 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. 344 1998 Higher dimensional continued fractions. Zbl 1044.11596Arnold, V. I. 20 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. 17 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 Mathematical problems of hydrodynamics and magnetohydrodynamics. Zbl 0999.76003Arnold, Vladimir 1 1998 Towards the Legendre Sturm theory of space curves. Zbl 0973.53505Arnold, 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 0885.70001Arnold, V. I.; Kozlov, V. V.; Neishtadt, A. I. 214 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. 10 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. 5 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. 4 1997 Topological classification of real trigonometric polynomials and cyclic serpents polyhedron. Zbl 0904.58007Arnold, V. 4 1997 Lectures on partial differential equations. Second edition. Zbl 1055.35500Arnol’d, V. I. 1 1997 The Arnold-Gelfand mathematical seminars. Zbl 0857.00029Arnold, V. I. (ed.); Gelfand, I. M. (ed.); Retakh, V. S. (ed.); Smirnov, M. (ed.) 1 1997 Topological classification of trigonometric polynomials and combinatorics of graphs with an equal number of vertices and edges. Zbl 0898.32019Arnold, V. I. 16 1996 Topological content of the Maxwell theorem on multipole representation of spherical functions. Zbl 0914.58003Arnold, V. 5 1996 Remarks on the extactic points of plane curves. Zbl 0990.58026Arnold, V. I. 4 1996 On the number of flattening points on space curves. Zbl 0973.53502Arnold, V. 3 1996 Singularities of caustics and wave fronts. Zbl 0929.53001Arnol’d, V. I. 2 1996 Topological problems of the theory of wave propagation. Zbl 1053.37500Arnol’d, V. I. 2 1996 Remarks on the enumeration of plane curves. Zbl 0973.53503Arnold, V. I. 2 1996 ...and 201 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 6,911 Authors 35 Marsden, Jerrold Eldon 33 Arnol’d, Vladimir Igorevich 32 Llibre, Jaume 31 Holm, Darryl D. 31 Markeev, Anatoliĭ Pavlovich 29 Broer, Henk W. 29 Neishtadt, Anatoly Iserovich 22 Kozlov, Valeriĭ Vasil’evich 21 Dobrokhotov, Sergei Yurievich 21 Khesin, Boris A. 21 Wiggins, Stephen 19 Ratiu, Tudor Stefan 18 Holmes, Philip J. 18 Preston, Stephen C. 17 Bruce, James William 17 Cruzeiro, Ana-Bela 17 Gaeta, Giuseppe 16 Celletti, Alessandra 16 Chierchia, Luigi 16 Dullin, Holger R. 16 Han, Maoan 16 Prykarpatsky, Anatoliy Karolevych 15 Froeschlé, Claude 15 Guzzo, Massimiliano 15 Janeczko, Stanisław 15 Peralta-Salas, Daniel 15 Yu, Pei 14 Fiedler, Bernold 14 Haller, George 13 Davydov, Alekseĭ Aleksandrovich 13 Enciso, Alberto 13 Izumiya, Shyuichi 13 Kolev, Boris 13 Luo, Shaokai 13 Misiołek, Gerard 13 Shafarevich, Andreĭ Igorevich 13 Shamolin, Maksim Vladimirovich 13 Tabachnikov, Serge L. 13 Vasil’ev, Viktor Anatol’evich 12 Albeverio, Sergio A. 12 Bauer, Martin 12 de la Llave, Rafael 12 de León Rodríguez, Manuel 12 Hanßmann, Heinz 12 Palacián, Jesús F. 12 Yanguas, Patricia 11 Brenier, Yann 11 Colin de Verdière, Yves 11 Delshams, Amadeu 11 Gay-Balmaz, François 11 Ghil, Michael 11 Giorgilli, Antonio 11 Kirillov, Oleg N. 11 Lega, Elena 11 Nazaikinskii, Vladimir E. 11 Sławianowski, Jan Jerzy 10 Aicardi, Francesca 10 Bloch, Anthony M. 10 Cardin, Franco 10 Escher, Joachim 10 Geng, Xianguo 10 Kuznetsov, Yuri Alexandrovich 10 Levi, Mark L. 10 Martín de Diego, David 10 Meiss, James D. 10 Mezić, Igor 10 Romero-Fuster, María Carmen 10 Sevryuk, Mikhail Borisovich 10 Sidorenko, Vladislav V. 10 Vasil’ev, Alekseĭ Alekseevich 10 Vidal, Claudio 10 Zhang, Xiang 9 Borisov, Alekseĭ Vladimirovich 9 Bounemoura, Abed 9 Ebeling, Wolfgang 9 Emch, Gerard G. 9 Gallavotti, Giovanni M. 9 Gavrilov, Lubomir 9 Greenblatt, Michael 9 Guckenheimer, John M. 9 Gusein-Zade, Sabir M. 9 Hoveijn, Igor 9 Ishikawa, Goo 9 Karpenkov, Oleg Nikolaevich 9 Kuksin, Sergeĭ B. 9 Lenells, Jonatan 9 Lerman, Lev 9 MacKay, Robert Sinclair 9 Mamaev, Ivan Sergeevich 9 Modin, Klas 9 Qi, Guoyuan 9 Rocha, Carlos 9 Sergeichuk, Vladimir Vasil’evich 9 Simó, Carles 9 Żołądek, Henryk 8 Artemyev, Anton V. 8 Bardin, Boris Sabirovich 8 Biasco, Luca 8 Blackmore, Denis L. 8 Bolotin, Sergeĭ Vladimirovich ...and 6,811 more Authors all top 5 Cited in 565 Serials 368 Physica D 236 Journal of Differential Equations 138 Journal of Mathematical Physics 134 Journal of Applied Mathematics and Mechanics 129 Communications in Mathematical Physics 129 Journal of Geometry and Physics 117 Physics Letters. 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Neuvième Série ...and 465 more Serials all top 5 Cited in 63 Fields 2,173 Dynamical systems and ergodic theory (37-XX) 1,257 Mechanics of particles and systems (70-XX) 893 Partial differential equations (35-XX) 871 Ordinary differential equations (34-XX) 771 Differential geometry (53-XX) 694 Fluid mechanics (76-XX) 669 Global analysis, analysis on manifolds (58-XX) 457 Quantum theory (81-XX) 397 Algebraic geometry (14-XX) 373 Manifolds and cell complexes (57-XX) 306 Several complex variables and analytic spaces (32-XX) 235 Numerical analysis (65-XX) 217 Statistical mechanics, structure of matter (82-XX) 186 Systems theory; control (93-XX) 144 Probability theory and stochastic processes (60-XX) 137 Number theory (11-XX) 128 Operator theory (47-XX) 127 Mechanics of deformable solids (74-XX) 127 Relativity and gravitational theory (83-XX) 121 Calculus of variations and optimal control; optimization (49-XX) 121 Biology and other natural sciences (92-XX) 119 Nonassociative rings and algebras (17-XX) 105 Optics, electromagnetic theory (78-XX) 98 Group theory and generalizations (20-XX) 94 Combinatorics (05-XX) 94 Topological groups, Lie groups (22-XX) 91 Linear and multilinear algebra; matrix theory (15-XX) 88 Algebraic topology (55-XX) 77 Computer science (68-XX) 63 Functional analysis (46-XX) 63 Convex and discrete geometry (52-XX) 58 Functions of a complex variable (30-XX) 56 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 48 Commutative algebra (13-XX) 48 Geophysics (86-XX) 45 Measure and integration (28-XX) 45 Difference and functional equations (39-XX) 43 Harmonic analysis on Euclidean spaces (42-XX) 42 Real functions (26-XX) 40 Associative rings and algebras (16-XX) 39 Information and communication theory, circuits (94-XX) 37 History and biography (01-XX) 35 Astronomy and astrophysics (85-XX) 34 Geometry (51-XX) 32 Approximations and expansions (41-XX) 32 General topology (54-XX) 31 Category theory; homological algebra (18-XX) 31 Classical thermodynamics, heat transfer (80-XX) 30 Operations research, mathematical programming (90-XX) 28 Statistics (62-XX) 22 General and overarching topics; collections (00-XX) 21 Special functions (33-XX) 17 Field theory and polynomials (12-XX) 17 Integral transforms, operational calculus (44-XX) 12 Abstract harmonic analysis (43-XX) 10 Mathematical logic and foundations (03-XX) 8 \(K\)-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) 3 Mathematics education (97-XX) 1 General algebraic systems (08-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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