WorldCat Identities

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

Works: 330 works in 1,411 publications in 8 languages and 20,974 library holdings
Genres: History  Biography  Anecdotes 
Roles: Author, Editor, Honoree, Illustrator, Dedicatee, Creator, Adapter
Classifications: QA614.58, 515.352
Publication Timeline
Most widely held works by V. I Arnolʹd
Ordinary differential equations by V. I Arnolʹd( Book )
60 editions published between 1973 and 2009 in 3 languages and held by 1,484 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 )
74 editions published between 1978 and 2011 in 3 languages and held by 1,438 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 approch, based on the theory of the geometry of manifolds, distinguishes iteself 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 )
49 editions published between 1983 and 2004 in 5 languages and held by 1,296 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
Geometrical methods in the theory of ordinary differential equations by V. I Arnolʹd( Book )
34 editions published between 1978 and 2004 in 3 languages and held by 1,014 WorldCat member libraries worldwide
Since the first edition of this book, geometrical methods in the theory of ordinary differential equations have become very popular and some progress has been made partly with the help of computers. Much of this progress is represented in this revised, expanded edition, including such topics as the Feigenbaum universality of period doubling, the Zoladec solution, the Iljashenko proof, the Ecalle and Voronin theory, the Varchenko and Hovanski theorems, and the Neistadt theory. In the selection of material for this book, the author explains basic ideas and methods applicable to the study of differential equations. Special efforts were made to keep the basic ideas free from excessive technicalities. Thus the most fundamental questions are considered in great detail, while of the more special and difficult parts of the theory have the character of a survey. Consequently, the reader needs only a general mathematical knowledge to easily follow this text. It is directed to mathematicians, as well as all users of the theory of differential equations
Singularity theory selected papers by V. I Arnolʹd( )
22 editions published between 1981 and 1993 in English and Undetermined and held by 976 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
Mathematical aspects of classical and celestial mechanics by V. I Arnolʹd( )
47 editions published between 1988 and 2009 in English and German and held by 784 WorldCat member libraries worldwide
"This work describes the fundamental principles, problems, and methods of classical mechanics. The main attention is devoted to the mathematical side of the subject. The authors have endeavored to give an exposition stressing the working apparatus of classical mechanics. The book is significantly expanded compared to the previous edition. The authors have added two chapters on the variational principles and methods of classical mechanics as well as on tensor invariants of equations of dynamics. Moreover, various other sections have been revised, added or expanded." "The main purpose of the book is to acquaint the reader with classical mechanics as a whole, in both its classical and its contemporary aspects. The book addresses all mathematicians, physicists and engineers."--Jacket
Topological methods in hydrodynamics by V. I Arnolʹd( Book )
28 editions published between 1899 and 2013 in English and Undetermined and held by 719 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
Arnold's problems by V. I Arnolʹd( )
27 editions published between 2004 and 2005 in English and held by 677 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. Many of these problems are still at the frontier of research today
Mathematics : frontiers and perspectives ( Book )
11 editions published between 1999 and 2000 in English and held by 598 WorldCat member libraries worldwide
Ergodic problems of classical mechanics by V. I Arnolʹd( Book )
22 editions published between 1968 and 1989 in English and Spanish and held by 584 WorldCat member libraries worldwide
Huygens and Barrow, Newton and Hooke : pioneers in mathematical analysis and catastrophe theory from evolvents to quasicrystals by V. I Arnol'd( Book )
12 editions published between 1989 and 1992 in English and Italian and held by 556 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
Lectures on partial differential equations by V. I Arnolʹd( Book )
14 editions published between 2004 and 2009 in English and German and held by 539 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 )
25 editions published between 1990 and 1993 in English and held by 500 WorldCat member libraries worldwide
Singularities of differentiable maps by V. I Arnolʹd( Book )
36 editions published between 1984 and 2012 in 3 languages and held by 464 WorldCat member libraries worldwide
Real algebraic geometry by V. I Arnolʹd( )
11 editions published in 2013 in English and held by 350 WorldCat member libraries worldwide
This book is concerned with one of the most fundamental questions of mathematics: the relationship between algebraic formulas and geometric images. At one of the first international mathematical 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 nineteenth 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)
Bifurcation theory and catastrophe theory by V. I Arnolʹd( Book )
33 editions published between 1991 and 2009 in English and German and held by 343 WorldCat member libraries worldwide
Bifurcation theory and catastrophe theory are two of the best known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Moreover, understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics", such as the characterization of personalities and the difference between a "genius" and a "maniac". Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, the first printing of which was published as Volume 5 of the Encyclopaedia of Mathematical Sciences, have given a masterly exposition of these two theories, with penetrating insight
Collected Works by V. I Arnolʹd( )
11 editions published in 2009 in English and held by 337 WorldCat member libraries worldwide
Trends and perspectives in applied mathematics by L Sirovich( Book )
2 editions published in 1994 in English and held by 308 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
The dynamics, statistics and projective geometry of Galois fields by V. I Arnolʹd( Book )
13 editions published between 2010 and 2011 in English and Undetermined and held by 291 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"--
Singularities of differentiable maps by V. I Arnolʹd( )
3 editions published in 2012 in English and held by 288 WorldCat member libraries worldwide
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Audience level: 0.69 (from 0.10 for Arnold, Vl ... to 1.00 for Solutions ...)
Alternative Names
Arnol′d Vladimir Igorevich 1937-2010
Arnol′d Vladimir Igorevitch 1937-2010
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
Arnold, Vl 1937-2010
Arnold Vladimir 1937-2010
Arnold, Vladimir I.
Arnolʹd, Vladimir I. 1937-2010
Arnolʹd, Vladimir Igorevič
Arnold, Vladimir Igorevič 1937-2010
Arnolʹd, Vladimir Igorevich
Arnolʹd, Vladimir Igorevich 1937-
Arnolʹd, Vladimir Igorevich 1937-2010
Arnold, W. I.
Арнольд, В. И 1937-2010
Арнольд, В. И. (Владимир Игоревич), 1937-2010
Арнольд, Владимир Игоревич.
Арнольд, Владимир Игоревич 1937-2010
アーノルド, V. I
English (522)
German (11)
Russian (7)
French (3)
Polish (2)
Spanish (2)
Italian (1)
Multiple languages (1)