WorldCat Identities

Arnolʹd, V. I. (Vladimir Igorevich) 1937-2010

Works: 236 works in 1,529 publications in 7 languages and 22,119 library holdings
Genres: History  Biography  Bibliography 
Roles: Author, Editor, Honoree, Other, Creator, Dedicatee, ed
Classifications: QA372, 515.352
Publication Timeline
Most widely held works by V. I Arnolʹd
Ordinary differential equations by I. G Petrovskiĭ( Book )

77 editions published between 1973 and 2009 in English and German and held by 2,215 WorldCat member libraries worldwide

Although there is no lack of other books on this subject, even with the same title, the appearance of this new one is fully justified on at least two grounds: its approach makes full use of modern mathematical concepts and terminology of considerable sophistication and abstraction, going well beyond the traditional presentation of the subject; and, at the same time, the resulting enhancement of mathematical abstractness is counterbalanced by a constant appeal to geometrical and physical considerations, presented in the main text and in numerous problems and exercises. In the terms of mathematical approach, the text is dominated by two central ideas: the theorem on rectifiability of a vector field (which is equivalent to the usual theorems on existence, uniqueness, and differentiability of solutions) and the theory of one-parameter groups of linear transformations (equivalent to the theory of linear autonomous systems). The book also develops whole congeries of fundamental concepts--like phase space and phase flows, smooth manifolds and tangent bundles, vector fields and one-parameter groups of diffeomorphisms--that remain in the shadows in the traditional coordinate-based approach. All of these concepts are presented in some detail, but without assuming any background on the part of the reader beyond the scope of the standard elementary courses on analysis and linear algebra
Mathematical methods of classical mechanics by V. I Arnolʹd( Book )

98 editions published between 1974 and 2014 in 5 languages and held by 1,613 WorldCat member libraries worldwide

In this text, the author constructs the mathematical apparatus of classical mechanics from the beginning, examining all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the Hamiltonian formalism. This modern approach, based on the theory of the geometry of manifolds, distinguishes itself from the traditional approach of standard textbooks. Geometrical considerations are emphasized throughout and include phase spaces and flows, vector fields, and Lie groups. The work includes a detailed discussion of qualitative methods of the theory of dynamical systems and of asymptotic methods like perturbation techniques, averaging, and adiabatic invariance
Catastrophe theory by V. I Arnolʹd( Book )

76 editions published between 1981 and 2009 in 6 languages and held by 1,325 WorldCat member libraries worldwide

"This short book, which is a translation from the original Russian, provides a concise, non-mathematical review of the less controversial results in catastrophe theory. The author begins by describing the established results in the theory of singularities and bifurcation and continues with chapters on the applications of the theory to topics such as wavefront propagation, the distribution of matter within the universe, and optimisation and control. The presentation is enhanced by numerous diagrams. ... This is a short, critical and non-mathematical review of catastrophe theory which will provide a useful introduction to the subject."--Physics Bulletin
Dynamical systems by V. I Arnolʹd( Book )

172 editions published between 1985 and 2010 in 4 languages and held by 1,073 WorldCat member libraries worldwide

This volume of the EMS is devoted to applications of singularity theory in mathematics and physics. The authors Arnol'd, Vasil'ev, Goryunov and Lyashkostudy bifurcation sets arising in various contexts such as the stability of singular points of dynamical systems, boundaries of the domains of ellipticity and hyperbolicity of partial differentail equations, boundaries of spaces of oscillating linear equations with variable coefficients and boundaries of fundamental systems of solutions. The book also treats applications of the following topics: functions on manifolds with boundary, projections of complete intersections, caustics, wave fronts, evolvents, maximum functions, shock waves, Petrovskij lacunas and generalizations of Newton's topological proof that Abelian integralsare transcendental. The book contains descriptions of numberous very recent research results that have not yet appeared in monograph form. There are also sections listing open problems, conjectures and directions offuture research. It will be of great interest for mathematicians and physicists, who use singularity theory as a reference and research aid
Ergodic problems of classical mechanics by V. I Arnolʹd( Book )

42 editions published between 1966 and 1999 in 4 languages and held by 860 WorldCat member libraries worldwide

Mathematics : frontiers and perspectives( Book )

12 editions published between 1999 and 2000 in English and held by 616 WorldCat member libraries worldwide

Huygens and Barrow, Newton and Hooke : pioneers in mathematical analysis and catastrophe theory from evolvents to quasicrystals by V. I Arnolʹd( Book )

19 editions published between 1989 and 1992 in 3 languages and held by 554 WorldCat member libraries worldwide

Translated from the Russian by E.J.F. Primrose "Remarkable little book."--SIAM REVIEW V.I. Arnold, who is renowned for his lively style, retraces the beginnings of mathematical analysis and theoretical physics in the works (and the intrigues!) of the great scientists of the 17th century. Some of Huygens' and Newton's ideas. several centuries ahead of their time, were developed only recently. The author follows the link between their inception and the breakthroughs in contemporary mathematics and physics. The book provides present-day generalizations of Newton's theorems on the elliptical shape of orbits and on the transcendence of abelian integrals; it offers a brief review of the theory of regular and chaotic movement in celestial mechanics, including the problem of ports in the distribution of smaller planets and a discussion of the structure of planetary rings
Singularities of differentiable maps by V. I Arnolʹd( Book )

61 editions published between 1985 and 2012 in English and German and held by 552 WorldCat member libraries worldwide

Lectures on partial differential equations by V. I Arnolʹd( Book )

20 editions published between 2004 and 2009 in English and German and held by 550 WorldCat member libraries worldwide

Arnold illustrates every principle with a figure. This book aims to cover the most basic parts of the subject and confines itself largely to the Cauchy and Neumann problems for the classical linear equations of mathematical physics, especially Laplace's equation and the wave equation, although the heat equation and the Korteweg-de Vries equation are also discussed. Physical intuition is emphasized. A large number of problems are sprinkled throughout the book, and a full set of problems from examinations given in Moscow are included at the end. Some of these problems are quite challenging!What makes the book unique is Arnold's particular talent at holding a topic up for examination from a new and fresh perspective. He likes to blow away the fog of generality that obscures so much mathematical writing and reveal the essentially simple intuitive ideas underlying the subject
The theory of singularities and its applications by V. I Arnolʹd( Book )

24 editions published between 1990 and 1993 in English and held by 511 WorldCat member libraries worldwide

Mathematical aspects of classical and celestial mechanics by V. I Arnolʹd( Book )

45 editions published between 1988 and 2009 in English and German and held by 428 WorldCat member libraries worldwide

Describes the fundamental principles, problems, and methods of classical mechanics. This book devotes its attention to the mathematical side of the subject. It aims to acquaint the reader with classical mechanics as a whole, in both its classical and its contemporary aspects
Topological methods in hydrodynamics by V. I Arnolʹd( Book )

31 editions published between 1899 and 2013 in English and Undetermined and held by 423 WorldCat member libraries worldwide

Topological hydrodynamics is a young branch of mathematics studying topological features of flows with complicated trajectories, as well as their applications to fluid motions. It is situated at the crossroad of hyrdodynamical stability theory, Riemannian and symplectic geometry, magnetohydrodynamics, theory of Lie algebras and Lie groups, knot theory, and dynamical systems. Applications of this approach include topological classification of steady fluid flows, descriptions of the Korteweg-de Vries equation as a geodesic flow, and results on Riemannian geometry of diffeomorphism groups, explaining, in particular, why longterm dynamical weather forecasts are not reliable. Topological Methods in Hydrodynamics is the first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics for a unified point of view. The necessary preliminary notions both in hydrodynamics and pure mathematics are described with plenty of examples and figures. The book is accessible to graduate students as well as to both pure and applied mathematicians working in the fields of hydrodynamics, Lie groups, dynamical systems and differential geometry
Singularity theory : selected papers by V. I Arnolʹd( Book )

18 editions published in 1981 in English and Undetermined and held by 391 WorldCat member libraries worldwide

Professor Arnold is a prolific and versatile mathematician who has done striking work in differential equations and geometrical aspects of analysis
Trends and perspectives in applied mathematics by L Sirovich( Book )

2 editions published in 1994 in English and held by 309 WorldCat member libraries worldwide

This will be the 100th volume of the Applied Mathematical Sciences series. In order to mark the occasion, this special volume has been created which will impact in an important way on the community that practices and is served by applied mathematics. Ten leading figures in the field present their own perspective of applied mathematics. The articles that are collected in this volume bear testimony to both the vitality and diversity of the subject. The contributors included here are: V.I. Arnol'd, Peter Constantin, Mitchell J. Feigenbaum, Martin Golubitsky, Daniel D. Joseph, Leo P. Kadanoff, Heinz-Otto Kreiss, H.P. McKean, Jerrold Marsden, and Roger Temam. The articles cover such topics as: mathematical problems in classical physics; geometric and analytic studies in turbulence; viscous and viscoelastic potential flow; difference methods for time dependent partial differential equations; geometric mechanics, stability and control. This special volume will be dedicated to Fritz John. John is one of the earliest advisors for the Springer- Verlag mathematics program, which includes his capacity as a series editor for the Applied Mathematical Sciences series. This volume appears in his honor
Arnold's problems by V. I Arnolʹd( Book )

21 editions published between 2000 and 2005 in English and German and held by 292 WorldCat member libraries worldwide

"Arnold's Problems contains mathematical problems which have been brought up by Vladimir Arnold in his famous seminar at Moscow State University over several decades. In addition, there are problems published in his numerous papers and books." "The invariable peculiarity of these problems was that mathematics was considered not as a game with deductive reasonings and symbols, but as a part of natural science (especially of physics), i.e. as an experimental science. Many of these problems are at the frontier of research still today and are still open, and even those that are mainly solved keep stimulating new research appearing every year in journals all over the world." "The second part of the book is a collection of comments of mostly Arnold's former students about the current progress in the problems' solution (featuring bibliography inspired by them)." "This book will be of great interest to researchers and graduate students in mathematics and mathematical physics."--Jacket
Topological invariants of plane curves and caustics by V. I Arnolʹd( Book )

16 editions published between 1944 and 2000 in English and held by 284 WorldCat member libraries worldwide

Dynamics, statistics and projective geometry of Galois fields by V. I Arnolʹd( Book )

15 editions published between 2010 and 2011 in English and Undetermined and held by 224 WorldCat member libraries worldwide

"V. I. Arnold reveals some unexpected connections between such apparently unrelated theories as Galois fields, dynamical systems, ergodic theory, statistics, chaos and the geometry of projective structures on finite sets. The author blends experimental results with examples and geometrical explorations to make these findings accessible to a broad range of mathematicians, from undergraduate students to experienced researchers"--
Tropical algebraic geometry by I. V Itenberg( Book )

14 editions published in 2013 in English and held by 109 WorldCat member libraries worldwide

"This book is concerned with one of the most fundamental question of mathematics: the relationship between algebraic formulas and geometric images. At one of the first international mathematic congresses (in Paris in 1900), Hilbert stated a special case of this question in the form of his 16th problem (from his list of 23 problems left over from the ninteenth century as a legacy for the twentieth century). In spite of the simplicity and importance of this problem (including its numerous applications), it remains unsolved to this day (although, as you will now see, many remarkable results have been discovered)"--Page 4 of cover
Collected works by V. I Arnolʹd( Book )

35 editions published between 1996 and 2013 in English and Undetermined and held by 84 WorldCat member libraries worldwide

"Vladimir Arnold is one of the greatest mathematical scientists of our time. He is famous for both the breadth and the depth of his work." "At the same time he is one of the most prolific and outstanding mathematical authors. This first volume of his Collected Works focuses on representations of functions, celestial mechanics, and KAM theory."--Jacket
Analysis and singularities : collected papers dedicated to Vladimir Igorevich Arnold on the occasion of his 70th birthday( Book )

9 editions published in 2007 in English and held by 13 WorldCat member libraries worldwide

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Mathematical methods of classical mechanics
Alternative Names
Arnol′d Vladimir Igorevich 1937-2010

Arnol′d Vladimir Igorevitch 1937-2010

Arnold 1937-2010 V.

Arnold, V.

Arnold, V. 1937-2010

Arnold , V. I.

Arnold, V. I. 1937-

Arnolʹd, V.I. 1937-2010

Arnolʹd, V. I. (Vladimir Igorevič), 1937-2010

Arnolʹd, V. I. (Vladimir Igorevich)

Arnol'd, V. I. (Vladimir Igorevich), 1937-

Arnold, Vl 1937-2010

Arnolʹd, Vladimir

Arnolʹd, Vladimir 1937-2010

Arnolʹd , Vladimir I.

Arnolʹd, Vladimir I. 1937-2010

Arnolʹd, Vladimir Igorevič

Arnolʹd, Vladimir Igorʹevič 1937-2010

Arnolʹd, Vladimir Igorevich

Arnolʹd, Vladimir Igorevich 1937-

Arnolʹd, Vladimir Igorevich 1937-2010

Arnold, W. I.

Vladimir Arnold mathématicien russe

Vladimir Arnold Russian mathematician

Vladimir Arnold Russisch wiskundige (1937-2010)

Vladimir Arnold russisk matematikar

Vladimir Arnold russisk matematiker

Vladimir Arnold rysk matematiker

Vladimir Igorevič Arnol'd matematico russo

Vladimir Igorevich Arnold

Vladimir Igorjevič Arnold

Vladimirs Arnolds

Vladimirus Arnold

Władimir Arnold

Wladimir Igorewitsch Arnold russischer Mathematiker

Βλαντιμίρ Άρνολντ Ρώσος μαθηματικός

Арнольд В. И. 1937-2010

Арнольд, В. И. (Владимир Игоревич)

Арнольд, В.И. (Владимир Игоревич), 1937-2010

Арнольд, Владимир Игоревич.

Арнольд, Владимир Игоревич 1937-2010

Арнольд Володимир Ігорович

Владимир Арнолд

ולדימיר ארנולד

فلاديمير أرنولد

ولادیمیر آرنولد ریاضی‌دان روسی

விளாதிமிர் ஆர்னோல்டு

블라디미르 아르놀트

アーノルド, V. I.



Mathematical methods of classical mechanicsCatastrophe theoryDynamical systemsMathematics : frontiers and perspectivesSingularities of differentiable mapsLectures on partial differential equationsThe theory of singularities and its applicationsMathematical aspects of classical and celestial mechanics