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## Arnol’d, Vladimir Igorevich

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 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
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#### 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 Neĭshtadt, Anatoliĭ 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, Anatoliĭ Sergeevich 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 Chernous’ko, Feliks Leonidovich 1 Chernyi, Gorimir Gorimirovich 1 Dalets’kyĭ, Yuriĭ L’vovych 1 Demidov, A. V. 1 Demidov, Sergeĭ Sergeevich 1 Egorov, Yuriĭ Vladimirovich 1 Eneev, T. M. 1 Filippov, Alexey F. 1 Frolov, Konstantin Vasilyevich 1 Galgani, Luigi 1 Gel’fand, E. M. 1 Glutsyuk, Alexey A. 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
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#### 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
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#### 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)

#### Citations contained in zbMATH Open

303 Publications have been cited 7,336 times in 6,222 Documents Cited by Year
Mathematical methods of classical mechanics. Translated by K. Vogtman and A. Weinstein. Zbl 0386.70001
Arnold, V. I.
1978
Sur la géométrie différentielle des groupes de Lie de dimension infinite et ses applications à l’hydrodynamique des fluides parfaits. Zbl 0148.45301
Arnol’d, V. I.
1966
Geometrical methods in the theory of ordinary differential equations. Transl. from the Russian by Joseph Szuecs, ed. by Mark Levi. Zbl 0507.34003
Arnold, V. I.
1983
Topological methods in hydrodynamics. Zbl 0902.76001
Arnold, V. I.; Khesin, B. A.
1998
Ergodic problems of classical mechanics. Zbl 0167.22901
Arnol’d, V. I.; Avez, A.
1968
Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by A. Iacob. 2nd printing of the 2nd ed. 1993. Zbl 0885.70001
Arnold, V. I.; Kozlov, V. V.; Neishtadt, A. I.
1997
Singularities of differentiable maps, Volume 2. Monodromy and asymptotics of integrals. Transl. from the Russian by Hugh Porteous and revised by the authors and James Montaldi. Reprint of the 1988 hardback edition. Zbl 1297.32001
Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N.
2012
Small denominators and problems of stability of motion in classical and celestial mechanics. Zbl 0135.42701
Arnol’d, V. I.
1963
Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by E. Khukhro. 3rd revised ed. Zbl 1105.70002
Arnold, Vladimir I.; Kozlov, Valery V.; Neishtadt, Anatoly I.
2006
Singularities of differentiable maps, Volume 1. Classification of critical points, caustics and wave fronts. Transl. from the Russian by Ian Porteous, edited by V. I. Arnol’d. Reprint of the 1985 hardback edition. Zbl 1290.58001
Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N.
2012
Proof of a theorem of A. N. Kolmogorov on the invariance of quasi-periodic motions under small perturbations of the Hamiltonian. Zbl 0129.16606
Arnol’d, V. I.
1963
Instability of dynamical systems with several degrees of freedom. Zbl 0135.42602
Arnol’d, V. I.
1964
Ordinary differential equations. Translated and edited by Richard A. Silverman. Zbl 0296.34001
Arnold, V. I.
1973
Small denominators. I: Mappings of the circumference onto itself. Zbl 0152.41905
Arnol’d, V. I.
1965
Mathematical methods of classical mechanics. Textbook. 3rd ed., rev. and compl. Zbl 0692.70003
Arnol’d, V. I.
1989
On matrices depending on parameters. Zbl 0259.15011
Arnol’d, V. I.
1972
Wave front evolution and equivariant Morse lemma. Zbl 0343.58003
Arnol’d, V. I.
1976
Ergodic problems of classical mechanics. Transl. from the French. Reprint. Zbl 0715.70004
Arnold, V. I.; Avez, A.
1989
Singularities of differentiable maps. Volume I: The classification of critical points, caustics and wave fronts. Transl. from the Russian by Ian Porteous, ed. by V. I. Arnol’d. Zbl 0554.58001
Arnol’d, V. I.; Gusejn-Zade, S. M.; Varchenko, A. N.
1985
Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields. Zbl 0411.58013
Arnol’d, V. I.
1977
Problèmes ergodiques de la mécanique classique. Zbl 0149.21704
Arnol’d, V. I.; Avez, A.
1967
Characteristic class entering in quantization conditions. Zbl 0175.20303
Arnol’d, V. I.
1967
The cohomology ring of the colored braid group. Zbl 0277.55002
Arnol’d, V. I.
1969
Index of a singular point of a vector field, the Petrovskii-Oleinik inequality, and mixed Hodge structures. Zbl 0407.57025
Arnol’d, V. I.
1978
Normal forms for functions near degenerate critical points, the Weyl groups of A$$_k$$, D$$_k$$, E$$_k$$ and lagrangian singularities. Zbl 0278.57011
Arnol’d, V. I.
1973
Sur la topologie des ecoulements stationnaires des fluides parfaits. Zbl 0145.22203
Arnol’d, V. I.
1965
Topological methods in hydrodynamics. Zbl 0743.76019
Arnold, V. I.; Khesin, B. A.
1992
Local normal forms of functions. Zbl 0336.57022
Arnold, V. I.
1976
Chapitres supplementaires de la théorie des équations différentielles ordinaires. Traduit du russe par Djilali Enbarek. Zbl 0455.34001
Arnold, V.
1980
Mathematical methods of classical mechanics. Zbl 0647.70001
Arnol’d, V. I.
1974
Singularities of differentiable maps. Volume II: Monodromy and asymptotics of integrals. Transl. from the Russian by Hugh Porteous. Zbl 0659.58002
Arnol’d, V. I.; Gusejn-Zade, S. M.; Varchenko, A. N.
1988
Les méthodes mathématiques de la mécanique classique. Traduit du russe par Djilali Embarek. Zbl 0385.70001
Arnol’d, V.
1976
Lectures on bifurcations in versal families. Zbl 0264.58005
Arnol’d, V. I.
1973
Ordinary differential equations. Zbl 0659.58012
Arnol’d, V. I.; Il’yashenko, Yu. S.
1988
Mathematical aspects of classical and celestial mechanics. Zbl 0612.70002
Arnol’d, V. I.; Kozlov, V. V.; Nejshtadt, A. I.
1985
Conditions for nonlinear stability of stationary plane curvilinear flows of an ideal fluid. Zbl 0141.43901
Arnol’d, V. I.
1965
Arnold’s problems. Translated and revised edition of the 2000 Russian original. Zbl 1051.00002
Arnold, V. I. (ed.)
2004
Dynamical systems I. Ordinary differential equations and smooth dynamical systems. Transl. from the Russian. Zbl 0658.00008
Anosov, D. V. (ed.); Arnold, V. I. (ed.); Gamkrelidze, R. V. (ed.)
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 0648.34002
Arnol’d, V. I.
1988
Supplementary chapters to the theory of ordinary differential equations. Zbl 0956.34503
Arnol’d, V. I.
1978
Remarks on singularities of finite codimension in complex dynamical systems. Zbl 0249.34035
Arnol’d, V. I.
1969
On an apriori estimate in the theory of hydrodynamical stability. Zbl 0191.56303
Arnol’d, V. I.
1969
Mathematical aspects of classical and celestial mechanics. Zbl 0674.70003
Arnol’d, V. I.; Kozlov, V. V.; Nejshtadt, A. I.
1987
Critical points of smooth functions and their normal forms. Zbl 0343.58001
Arnol’d, V. I.
1975
First steps in symplectic topology. Zbl 0649.58010
Arnol’d, V. I.
1986
Plane curves, their invariants, perestroikas and classifications. Zbl 0864.57027
Arnold, V. I.
1994
Singularities of caustics and wave fronts. Transl. from the Russian. Zbl 0734.53001
Arnol’d, V. I.
1990
The asymptotic Hopf invariant and its applications. Zbl 0623.57016
Arnol’d, V. I.
1986
Some algebro-geometrical aspects of the Newton attraction theory. Zbl 0569.58018
Arnol’d, V. I.
1983
Modes and quasimodes. Zbl 0251.70012
Arnol’d, V. I.
1972
Normal forms of functions in neighbourhoods of degenerate critical points. Zbl 0304.57018
Arnol’d, V. I.
1974
Remarks on the perturbation theory for problems of Mathieu type. Zbl 0541.34035
Arnol’d, V. I.
1983
Symplectic geometry. Zbl 0780.58016
Arnol’d, V. I.; Givental’, A. B.
1985
Some unsolved problems in the theory of differential equations and mathematical physics. Zbl 0703.35002
Arnol’d, V. I.; Vishik, M. I.; Il’yashenko, Yu. S.; Kalashnikov, A. S.; Kondrat’ev, V. A.; Kruzhkov, S. N.; Landis, E. M.; Millionshchikov, V. M.; Oleĭnik, O. A.; Filippov, A. F.; Shubin, M. A.
1989
The Sturm theorems and symplectic geometry. Zbl 0606.58017
Arnol’d, V. I.
1985
Sur une propriété topologique des applications golbalement canoniques de la mécanique classique. Zbl 0134.42305
Arnol’d, V. I.
1965
The geometry of spherical curves and the algebra of quaternions. Zbl 0848.58005
Arnol’d, V. I.
1995
Indices of singular points of 1-forms on a manifold with boundary, convolution of invariants of reflection groups, and singular projections of smooth surfaces. Zbl 0431.58010
Arnol’d, V. I.
1979
Statistics of integral convex polygons. Zbl 0447.52011
Arnol’d, V. I.
1980
Catastrophe theory. Transl. from the Russian by R. K. Thomas. Zbl 0517.58003
Arnold, V. I.
1984
Topological classification of Morse functions and generalisations of Hilbert’s 16-th problem. Zbl 1149.57044
Arnold, Vladimir I.
2007
Higher dimensional continued fractions. Zbl 1044.11596
Arnold, V. I.
1998
Remarks on eigenvalues and eigenvectors of Hermitian matrices, Berry phase, adiabatic connections and quantum Hall effect. Zbl 0841.58008
Arnold, V. I.
1995
Singularity theory. Selected papers. Zbl 0457.58002
Arnold, V. I.
1981
On functions of three variables. Zbl 0090.27101
Arnol’d, V. I.
1957
Kolmogorov’s hydrodynamic attractors. Zbl 0726.76045
Arnol’d, V. I.
1991
Dynamics of complexity of intersections. Zbl 0782.54020
Arnold, V. I.
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 0296.34002
Arnold, V.
1974
The stability of the equilibrium position of a Hamiltonian system of ordinary differential equations in the general elliptic case. Zbl 0135.42601
Arnol’d, V. I.
1961
Singularity theory I. Transl. from the Russian by A. Iacob. 2nd printing of the 1st ed. 1993. Zbl 0901.58001
Arnold, V. I.; Goryunov, V. V.; Lyashko, O. V.; Vasil’ev, V. A.
1998
Topological invariants of plane curves and caustics. Zbl 0858.57001
Arnol’d, Vladimir Igorevich
1994
Topological and ergodic properties of closed 1-forms with incommensurable periods. Zbl 0732.58001
Arnol’d, V. I.
1991
A-graded algebras and continued fractions. Zbl 0692.16012
Arnol’d, V. I.
1989
Supplementary chapters to the theory of ordinary differential equations. Zbl 0956.34501
Arnol’d, V.
1980
Singularities of smooth mappings. Zbl 0167.21702
Arnol’d, V. I.
1968
Topological classification of trigonometric polynomials and combinatorics of graphs with an equal number of vertices and edges. Zbl 0898.32019
Arnold, V. I.
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 0415.58004
Arnol’d, V. I.
1978
Sur un principe variationnel pour les ecoulements stationnaires des liquides parfaits et ses applications aux problèmes de stabilité non linéaires. Zbl 0161.22903
Arnol’d, V. I.
1966
Lectures on partial differential equations. Zbl 1076.35001
Arnold, V. I.
2004
Ordinary differential equations. Transl. from the 3rd Russian ed. by Roger Cooke. Zbl 0744.34001
Arnol’d, Vladimir I.
1992
A branched covering of $$CP^ 2\to S^ 4$$, hyperbolicity and projectivity topology. Zbl 0721.57003
Arnol’d, V. I.
1988
Mathematical problems in classical physics. Zbl 0806.53078
Arnold, V. I.
1994
Bernoulli-Euler updown numbers associated with function singularities, their combinatorics and arithmetics. Zbl 0755.58015
Arnol’d, V. I.
1991
Remarks on the stationary phase method and Coxeter numbers. Zbl 0291.40005
Arnol’d, V. I.
1973
The calculus of snakes and the combinatorics of Bernoulli, Euler, and Springer numbers of Coxeter groups. Zbl 0791.05001
Arnol’d, V. I.
1992
Cardiac arrythmias and circle mappings. Zbl 0900.92094
Arnold, V. I.
1991
Newton’s Principia read 300 years later. Zbl 0693.01005
Arnol’d, V. I.; Vasil’ev, V. A.
1989
Weak asymptotics for the numbers of solutions of Diophantine problems. Zbl 1042.11064
Arnol’d, V. I.
1999
Some remarks on symplectic monodromy of Milnor fibrations. Zbl 0970.53043
Arnold, V. I.
1995
Catastrophe theory. Translated from the Russian by G. S. Wassermann. Based on the translation by R. K. Thomas. 3. rev. and exp. ed. Zbl 0746.58001
Arnol’d, V. I.
1992
Ordinary differential equations. Textbook. (Obyknovennye differentsial’nye uravneniya. Uchebnoe posobie). 3rd ed., rev. and compl. Zbl 0577.34001
Arnol’d, V. I.
1984
Singularities of systems of rays. Zbl 0531.58009
Arnol’d, V. I.
1983
Some remarks on flows of line elements and frames. Zbl 0124.14601
Arnol’d, V. I.
1961
The topology of algebra: Combinatorics of squaring. Zbl 1040.05015
Arnold, V. I.
2003
Catastrophe theory. Zbl 0797.58002
Arnol’d, V. I.
1986
Bifurcation theory. Zbl 0797.58003
Arnol’d, V. I.; Afrajmovich, V. S.; Il’yashenko, Yu. S.; Shil’nikov, L. P.
1986
Ordinary differential equations. Transl. and ed. by Richard A. Silverman. 1st paperback ed., 2nd printing. Zbl 0432.34001
Arnold, V. I.
1980
Variational principle for three-dimensional steady-state flows of an ideal fluid. Zbl 0163.19807
Arnol’d, V. I.
1965
Arithmetics of binary quadratic forms, symmetry of their continued fractions and geometry of their de Sitter world. Zbl 1044.11016
Arnold, V.
2003
Optimization in mean and phase transitions in controlled dynamical systems. Zbl 1057.49003
Arnol’d, V. I.
2002
Experimental mathematics. Zbl 1323.00003
Arnold, V. I.
2015
Lectures and problems: a gift to young mathematicians. Translated by Dmitry Fuchs and Mark Saul. Zbl 1331.00009
Arnold, V. I.
2015
Vladimir I. Arnold – Collected works. Vol. II. Hydrodynamics, bifurcation theory, and algebraic geometry 1965–1972. Edited by Alexander B. Givental, Boris A. Khesin, Alexander N. Varchenko, Victor A. Vassiliev and Oleg Ya. Viro. Zbl 1354.01038
Arnold, Vladimir I.
2014
Mathematical understanding of nature. Essays on amazing physical phenomena and their understanding by mathematicians. Translated from the Russian by Alexei Sossinsky and Olga Sipacheva. Zbl 1302.00049
Arnold, V. I.
2014
Singularities of differentiable maps, Volume 2. Monodromy and asymptotics of integrals. Transl. from the Russian by Hugh Porteous and revised by the authors and James Montaldi. Reprint of the 1988 hardback edition. Zbl 1297.32001
Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N.
2012
Singularities of differentiable maps, Volume 1. Classification of critical points, caustics and wave fronts. Transl. from the Russian by Ian Porteous, edited by V. I. Arnol’d. Reprint of the 1985 hardback edition. Zbl 1290.58001
Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N.
2012
Singularities of functions, wave fronts, caustics and multidimensional integrals. Zbl 1255.58002
Arnold, V. I.; Varchenko, A. N.; Givental, A. B.; Khovanskii, A. G.
2012
Topological properties of eigenoscillations in mathematical physics. Zbl 1229.35220
Arnold, V. I.
2011
Dynamics, statistics and projective geometry of Galois fields. Zbl 1219.00001
Arnold, V. I.
2011
Topological classification of Morse polynomials. Zbl 1214.57026
Arnold, V. I.
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 1187.01033
Arnold, Vladimir I.
2010
Stochastic and deterministic characteristics of orbits in chaotically looking dynamical systems. Zbl 1211.37007
Arnold, V. I.
2009
Geometry of continued fractions associated with Frobenius numbers. Zbl 1201.11009
Arnold, Vladimir I.
2009
Lengths of periods of continued fractions of square roots of integers. Zbl 1208.11013
Arnold, Vladimir I.
2009
Permutations. Zbl 1230.05283
Arnold, V. I.
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.
2009
Empirical study of stochasticity for deterministic chaotical dynamics of geometric progressions of residues. Zbl 1184.37011
Arnold, Vladimir I.
2009
Uniform distribution of non-divisible vectors in an integer space. Zbl 1241.11088
Arnold, V. I.
2009
Statistics of the periods of continued fractions for quadratic irrationals. Zbl 1152.11002
Arnol’d, V. I.
2008
Orbits’ statistics in chaotic dynamical systems. Zbl 1161.37039
Arnold, V.
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.
2008
Topological classification of Morse functions and generalisations of Hilbert’s 16-th problem. Zbl 1149.57044
Arnold, Vladimir I.
2007
Continued fractions of square roots of rational numbers and their statistics. Zbl 1147.11036
Arnol’d, V. I.
2007
Arithmetical turbulence of selfsimilar fluctuations statistics of large Frobenius numbers of additive semigroups of integers. Zbl 1232.11046
Arnold, V.
2007
Topological classification of trigonometric polynomials related to the affine Coxeter group $$\widetilde A_2$$. Zbl 1196.58004
Arnold, V. I.
2007
Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by E. Khukhro. 3rd revised ed. Zbl 1105.70002
Arnold, Vladimir I.; Kozlov, Valery V.; Neishtadt, Anatoly I.
2006
Complexity of finite sequences of zeros and ones and geometry of finite spaces of functions. Zbl 1196.11033
Arnold, Vladimir I.
2006
Geometry and growth rate of Frobenius numbers of additive semigroups. Zbl 1141.11020
Arnold, V. I.
2006
Forgotten and neglected theories of Poincaré. Zbl 1165.01013
Arnol’d, V. I.
2006
On the matricial version of Fermat-Euler congruences. Zbl 1168.05003
Arnold, V. I.
2006
Smooth functions statistics. Zbl 1154.26018
Arnold, Vladimir I.
2006
Statistics of the symmetric group representations as a natural science question on asymptotics of Young diagrams. Zbl 1171.20305
Arnold, Vladimir
2006
Statistics of Young diagrams of cycles of dynamical systems for finite tori automorphisms. Zbl 1124.05096
Arnold, V.
2006
From Hilbert’s superposition problem to dynamical systems. Zbl 1096.01007
Arnold, V. I.
2006
Lobachevsky triangle altitudes theorem as the Jacobi identity in the Lie algebra of quadratic forms on symplectic plane. Zbl 1092.53055
Arnold, V.
2005
Number-theoretical turbulence in Fermat-Euler arithmetics and large Young diagrams geometry statistics. Zbl 1134.11344
Arnold, V.
2005
Ergodic and arithmetical properties of geometrical progression’s dynamics and of its orbits. Zbl 1089.11004
Arnold, V.
2005
On the topology of the eigenfields. Zbl 1134.35300
Arnold, Vladimir I.
2005
Arnold’s problems. Translated and revised edition of the 2000 Russian original. Zbl 1051.00002
Arnold, V. I. (ed.)
2004
Lectures on partial differential equations. Zbl 1076.35001
Arnold, V. I.
2004
Fermat dynamics, matrix arithmetics, finite circles, and finite Lobachevsky planes. Zbl 1125.11066
Arnold, V. I.
2004
Lectures on partial differential equations. Transl. from the Russian by Roger Cooke. Zbl 1076.35002
Arnold, Vladimir I.
2004
Geometry and dynamics of Galois fields. Zbl 1148.37301
Arnol’d, V. I.
2004
The matrix Euler-Fermat theorem. Zbl 1167.11300
Arnol’d, V. I.
2004
From Hilbert’s superposition problem to dynamical systems. Zbl 1187.01024
Arnol’d, V. I.
2004
Ol’ga Aleksandrovna Ladyzhenskaya (obituary). Zbl 1062.01503
Arnol’d, V. I.; Birman, M. Sh.; Vershik, A. M.; et al.
2004
The topology of algebra: Combinatorics of squaring. Zbl 1040.05015
Arnold, V. I.
2003
Arithmetics of binary quadratic forms, symmetry of their continued fractions and geometry of their de Sitter world. Zbl 1044.11016
Arnold, V.
2003
Aleksej Vasil’evich Pogorelov (obituary). Zbl 1050.01509
Aleksandrov, V. A.; Arnol’d, V. I.; Borisenko, A. A.; et al.
2003
Fermat-Euler dynamical systems and the statistics of arithmetics of geometric progressions. Zbl 1038.11006
Arnold, V. I.
2003
Topology and statistics of formulas of arithmetic. Zbl 1124.11304
Arnol’d, V. I.
2003
Frequent representations. Zbl 1075.20004
Arnold, V. I.
2003
Optimization in mean and phase transitions in controlled dynamical systems. Zbl 1057.49003
Arnol’d, V. I.
2002
Pseudoquaternion geometry. Zbl 1039.53082
Arnol’d, V. I.
2002
Astroidal geometry of hypercycloids and the Hessian topology of hyperbolic polynomials. Zbl 1058.58018
Arnol’d, V. I.
2001
Dynamical systems. IV. Symplectic geometry and its applications. Transl. from the Russian by G. Wassermann. 2nd, expanded and revised ed. Zbl 1048.00010
Arnold, V. I. (ed.); Novikov, S. P. (ed.); Gamkrelidze, R. V. (ed.)
2001
Lagrangian Grassmannian of a quaternion hypersymplectic space. Zbl 1034.53081
Arnol’d, V. I.
2001
On teaching mathematics. Zbl 1242.00021
Arnold, Vładimir I.
2001
Complexification of tetrahedron and pseudo-projective transformations. Zbl 0999.51001
Arnold, V. I.
2001
Symplectic geometry and topology. Zbl 1021.53053
Arnold, V. I.
2000
Mathematics: frontiers and perspectives. Zbl 1047.00015
Arnold, V. (ed.); Atiyah, M. (ed.); Lax, P. (ed.); Mazur, B. (ed.)
2000
Arnold’s problems. Zbl 1052.00003
Arnol’d, V. I.
2000
The complex Lagrangian Grassmannian. Zbl 0996.53051
Arnold, V. I.
2000
Polymathematics: is mathematics a single science or a set of arts? Zbl 0980.00004
Arnold, V. I.
2000
Dynamical systems. Zbl 0963.37003
Arnold, Vladimir
2000
Euler, Bernoulli and Springer numbers for Coxeter groups and Morse spaces: snake calculus. Zbl 1080.05501
Arnold, Vladimir I.
2000
From averaging to statistical physics. Zbl 1034.82001
Arnol’d, V. I.
2000
Singularity theory. Zbl 0971.58022
Arnold, Vladimir
2000
Weak asymptotics for the numbers of solutions of Diophantine problems. Zbl 1042.11064
Arnol’d, V. I.
1999
Bifurcation theory and catastrophe theory. Translated from the 1986 Russian original by N. D. Kazarinoff. Reprint of the original English edition from the series Encyclopaedia of Mathematical Sciences (Dynamical systems V), 5 (1994). Zbl 1038.37500
Arnold, V. I.; Afraĭmovich, V. S.; Il’yashenko, Yu. S.; Shil’nikov, L. P.
1999
Simple singularities of curves. Zbl 0991.32015
Arnol’d, V. I.
1999
From Hilbert’s superposition problem to dynamical systems. Zbl 0967.01012
Arnold, V. I.
1999
Symplectization, complexification and mathematical trinities. Zbl 0948.01012
Arnold, V. I.
1999
First steps of local contact algebra. Zbl 1031.53110
Arnold, V. I.
1999
Ergodic problems of classical mechanics. Transl. from the French and the English by A. V. Borisov, Yu. A. Danilov, A. V. Letchikov, I. S. Mamaev. Zbl 0974.70003
Arnold, V. I.; Avez, A.
1999
Topological problems of the theory of asymptotic curves. Zbl 1010.37012
Arnold, V. I.
1999
First step of local symplectic algebra. Zbl 0970.57015
Arnold, V. I.
1999
Pseudoperiodic topology. With a preface (ix–xii) by V. I. Arnold. Zbl 0931.00017
Arnold, V. (ed.); Kontsevich, M. (ed.); Zorich, A. (ed.)
1999
Relatives of the quotient of the complex projective plane by the complex conjugation. Zbl 0963.53023
Arnold, V. I.
1999
Topological problems in wave propagation theory and topological economy principle in algebraic geometry. Zbl 0946.01011
Arnold, V. I.
1999
Topological methods in hydrodynamics. Zbl 0902.76001
Arnold, V. I.; Khesin, B. A.
1998
Higher dimensional continued fractions. Zbl 1044.11596
Arnold, V. I.
1998
Singularity theory I. Transl. from the Russian by A. Iacob. 2nd printing of the 1st ed. 1993. Zbl 0901.58001
Arnold, V. I.; Goryunov, V. V.; Lyashko, O. V.; Vasil’ev, V. A.
1998
On teaching mathematics. Zbl 1114.00300
Arnold, V. I.
1998
On the problem of realization of a given Gaussian curvature function. Zbl 0935.53001
Arnold, Vladimir
1998
Mathematical problems of hydrodynamics and magnetohydrodynamics. Zbl 0999.76003
Arnold, Vladimir
1998
Towards the Legendre Sturm theory of space curves. Zbl 0973.53505
Arnold, V. I.
1998
Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by A. Iacob. 2nd printing of the 2nd ed. 1993. Zbl 0885.70001
Arnold, V. I.; Kozlov, V. V.; Neishtadt, A. I.
1997
Ordinary differential equations and smooth dynamical systems. Transl. from the Russian by E. R. Dawson and D. O’Shea. 3rd printing of the 1st ed. 1988. Zbl 0858.34001
Anosov, D. V.; Aranson, S. Kh.; Arnold, V. I.; Bronshtein, I. U.; Grines, V. Z.; Il’yashenko, Yu. S.
1997
Remarks on the parabolic curves on surfaces and on the higher-dimensional Möbius-Sturm theory. Zbl 0973.53504
Arnold, V. I.
1997
Separated Dirac operators and asymptotically constant linear systems. Zbl 0902.34073
Arnold, V.; Kalf, H.; Schneider, A.
1997
Remarks concerning the Morse theory of a divergence-free vector field, the averaging method, and the motion of a charged particle in a magnetic field. Zbl 0923.58010
Arnol’d, V. I.
1997
Topological classification of real trigonometric polynomials and cyclic serpents polyhedron. Zbl 0904.58007
Arnold, V.
1997
Lectures on partial differential equations. Second edition. Zbl 1055.35500
Arnol’d, V. I.
1997
The Arnold-Gelfand mathematical seminars. Zbl 0857.00029
Arnold, V. I. (ed.); Gelfand, I. M. (ed.); Retakh, V. S. (ed.); Smirnov, M. (ed.)
1997
Topological classification of trigonometric polynomials and combinatorics of graphs with an equal number of vertices and edges. Zbl 0898.32019
Arnold, V. I.
1996
Topological content of the Maxwell theorem on multipole representation of spherical functions. Zbl 0914.58003
Arnold, V.
1996
Remarks on the extactic points of plane curves. Zbl 0990.58026
Arnold, V. I.
1996
On the number of flattening points on space curves. Zbl 0973.53502
Arnold, V.
1996
Singularities of caustics and wave fronts. Zbl 0929.53001
Arnol’d, V. I.
1996
...and 203 more Documents
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#### Cited by 6,955 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 Neĭshtadt, Anatoliĭ Iserovich 22 Dobrokhotov, Sergei Yurievich 22 Khesin, Boris A. 22 Kozlov, Valeriĭ Vasil’evich 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 15 Froeschlé, Claude 15 Guzzo, Massimiliano 15 Janeczko, Stanisław 15 Peralta-Salas, Daniel 15 Prykarpatsky, Anatoliy Karolevych 15 Yu, Pei 14 Fiedler, Bernold 14 Haller, George 14 Tabachnikov, Serge L. 14 Vasil’ev, Viktor Anatol’evich 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 12 Albeverio, Sergio A. 12 Bauer, Martin 12 de la Llave, Rafael 12 de León Rodríguez, Manuel 12 Hanßmann, Heinz 12 Kalyakin, Leonid Anatol’evich 12 Nazaikinskii, Vladimir E. 12 Palacián, Jesús F. 12 Yanguas, Patricia 11 Bloch, Anthony M. 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 Sławianowski, Jan Jerzy 10 Aicardi, Francesca 10 Cardin, Franco 10 Escher, Joachim 10 Geng, Xianguo 10 Kuksin, Sergeĭ B. 10 Kuznetsov, Yuri Alexandrovich 10 Levi, Mark L. 10 Mamaev, Ivan Sergeevich 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 Bolotin, Sergeĭ Vladimirovich 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 Lenells, Jonatan 9 Lerman, Lev 9 MacKay, Robert Sinclair 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 ...and 6,855 more Authors
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#### Cited in 566 Serials

 368 Physica D 238 Journal of Differential Equations 139 Journal of Mathematical Physics 134 Journal of Applied Mathematics and Mechanics 131 Journal of Geometry and Physics 130 Communications in Mathematical Physics 117 Physics Letters. A 110 Functional Analysis and its Applications 101 Journal of Mathematical Analysis and Applications 97 Chaos, Solitons and Fractals 89 Regular and Chaotic Dynamics 81 Journal of Mathematical Sciences (New York) 78 Annales de l’Institut Fourier 75 Celestial Mechanics and Dynamical Astronomy 69 Advances in Mathematics 68 Archive for Rational Mechanics and Analysis 66 Chaos 63 Annals of Physics 60 Reports on Mathematical Physics 60 Proceedings of the Steklov Institute of Mathematics 58 Duke Mathematical Journal 53 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 52 Journal of Statistical Physics 49 Mathematical Notes 49 Inventiones Mathematicae 47 Prikladnaya Matematika i Mekhanika 47 Linear Algebra and its Applications 46 Nuclear Physics. B 44 Theoretical and Mathematical Physics 44 Mathematische Annalen 42 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 40 Topology and its Applications 39 Journal of Fluid Mechanics 39 Journal of Functional Analysis 39 Transactions of the American Mathematical Society 39 Journal of Nonlinear Science 37 Bulletin des Sciences Mathématiques 35 Nonlinear Analysis. Theory, Methods & Applications 34 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 33 Applied Mathematics and Computation 33 Nonlinear Dynamics 33 Journal of High Energy Physics 32 Journal of Computational and Applied Mathematics 32 Differential Geometry and its Applications 32 Annales de l’Institut Henri Poincaré. Physique Théorique 31 Compositio Mathematica 31 Discrete and Continuous Dynamical Systems 30 Mathematische Zeitschrift 30 Journal of Nonlinear Mathematical Physics 29 Journal of Soviet Mathematics 28 Computers & Mathematics with Applications 28 Mathematical Proceedings of the Cambridge Philosophical Society 28 Ergodic Theory and Dynamical Systems 28 Systems & Control Letters 27 Arnold Mathematical Journal 26 Physica A 26 Comptes Rendus. Mathématique. Académie des Sciences, Paris 25 Nonlinearity 25 Acta Applicandae Mathematicae 25 Journal of Dynamics and Differential Equations 25 Communications in Nonlinear Science and Numerical Simulation 24 Celestial Mechanics 24 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 24 Journal of Dynamical and Control Systems 23 Israel Journal of Mathematics 23 Journal of Computational Physics 23 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 23 Functional Analysis and Other Mathematics 22 Geometriae Dedicata 22 Manuscripta Mathematica 21 International Journal of Theoretical Physics 21 Letters in Mathematical Physics 21 Russian Journal of Mathematical Physics 21 Journal of Geometric Mechanics 20 ZAMP. Zeitschrift für angewandte Mathematik und Physik 20 Annali di Matematica Pura ed Applicata. Serie Quarta 20 Algebraic & Geometric Topology 20 Journal of Physics A: Mathematical and Theoretical 19 Communications on Pure and Applied Mathematics 19 Journal of Algebra 19 Proceedings of the American Mathematical Society 19 Indagationes Mathematicae. New Series 19 Qualitative Theory of Dynamical Systems 19 SIAM Journal on Applied Dynamical Systems 18 Bulletin of the American Mathematical Society. New Series 18 Geometry & Topology 17 Acta Mechanica 17 Physics of Fluids 17 Journal of Pure and Applied Algebra 17 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 17 Annals of Mathematics. Second Series 16 Computer Methods in Applied Mechanics and Engineering 16 General Relativity and Gravitation 16 Automatica 16 Acta Mathematica Sinica. English Series 16 Nonlinear Analysis. Real World Applications 15 Journal of Symbolic Computation 15 Geometric and Functional Analysis. GAFA 15 Communications in Partial Differential Equations 15 Journal de Mathématiques Pures et Appliquées. Neuvième Série ...and 466 more Serials
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#### Cited in 63 Fields

 2,182 Dynamical systems and ergodic theory (37-XX) 1,269 Mechanics of particles and systems (70-XX) 898 Partial differential equations (35-XX) 875 Ordinary differential equations (34-XX) 774 Differential geometry (53-XX) 697 Fluid mechanics (76-XX) 673 Global analysis, analysis on manifolds (58-XX) 461 Quantum theory (81-XX) 403 Algebraic geometry (14-XX) 375 Manifolds and cell complexes (57-XX) 309 Several complex variables and analytic spaces (32-XX) 239 Numerical analysis (65-XX) 216 Statistical mechanics, structure of matter (82-XX) 186 Systems theory; control (93-XX) 144 Probability theory and stochastic processes (60-XX) 138 Number theory (11-XX) 128 Operator theory (47-XX) 127 Relativity and gravitational theory (83-XX) 126 Mechanics of deformable solids (74-XX) 122 Biology and other natural sciences (92-XX) 121 Calculus of variations and optimal control; optimization (49-XX) 120 Nonassociative rings and algebras (17-XX) 106 Optics, electromagnetic theory (78-XX) 99 Group theory and generalizations (20-XX) 96 Combinatorics (05-XX) 95 Topological groups, Lie groups (22-XX) 91 Linear and multilinear algebra; matrix theory (15-XX) 90 Algebraic topology (55-XX) 77 Computer science (68-XX) 66 Convex and discrete geometry (52-XX) 63 Functional analysis (46-XX) 57 Functions of a complex variable (30-XX) 56 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 49 Geophysics (86-XX) 48 Commutative algebra (13-XX) 47 Measure and integration (28-XX) 46 Real functions (26-XX) 44 Difference and functional equations (39-XX) 44 Harmonic analysis on Euclidean spaces (42-XX) 40 Associative rings and algebras (16-XX) 39 Information and communication theory, circuits (94-XX) 37 History and biography (01-XX) 36 Geometry (51-XX) 35 Astronomy and astrophysics (85-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) 23 General and overarching topics; collections (00-XX) 22 Special functions (33-XX) 17 Field theory and polynomials (12-XX) 16 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)

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