WorldCat Identities

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

Overview
Works: 291 works in 1,844 publications in 8 languages and 25,294 library holdings
Genres: History  Biography  Bibliography 
Roles: Author, Editor, Honoree, Other, Creator, Dedicatee, Adapter, Thesis advisor, ed
Classifications: QA372, 515.352
Publication Timeline
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Most widely held works by V. I Arnolʹd
Ordinary differential equations by V. I Arnolʹd( Book )

148 editions published between 1971 and 2012 in 5 languages and held by 1,779 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 )

107 editions published between 1974 and 2014 in 5 languages and held by 1,668 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 )

83 editions published between 1981 and 2009 in 7 languages and held by 1,331 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 )

42 editions published between 1982 and 2012 in English and German and held by 1,029 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
Ergodic problems of classical mechanics by V. I Arnolʹd( Book )

46 editions published between 1966 and 1999 in 4 languages and held by 882 WorldCat member libraries worldwide

Mathematics : frontiers and perspectives( Book )

15 editions published between 1999 and 2000 in English and held by 649 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 )

22 editions published between 1989 and 1992 in 3 languages and held by 633 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 )

21 editions published between 2004 and 2009 in English and German and held by 600 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
Mathematical aspects of classical and celestial mechanics by V. I Arnolʹd( Book )

55 editions published between 1988 and 2009 in English and German and held by 473 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 )

33 editions published between 1899 and 2009 in English and Undetermined and held by 461 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
Bifurcation theory and catastrophe theory by V. I Arnolʹd( Book )

43 editions published between 1991 and 2009 in 3 languages and held by 426 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
Singularity theory : selected papers by V. I Arnolʹd( Book )

25 editions published in 1981 in English and Undetermined and held by 397 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
Dynamical systems by V. I Arnolʹd( Book )

43 editions published between 1988 and 1998 in 4 languages and held by 360 WorldCat member libraries worldwide

A survey of singularity theory and its main applications. It covers: the critical points of functions; monodromy groups of critical points; basic properties of maps; and the global theory of singularities
Arnold's problems by V. I Arnolʹd( Book )

31 editions published between 2000 and 2006 in English and German and held by 353 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
Dynamical systems IV : symplectic geometry and its applications by V. I Arnolʹd( Book )

47 editions published between 1985 and 2001 in English and German and held by 349 WorldCat member libraries worldwide

This book takes a snapshot of the mathematical foundations of classical and quantum mechanics from a contemporary mathematical viewpoint. It covers a number of important recent developments in dynamical systems and mathematical physics and places them in the framework of the more classical approaches; the presentation is enhanced by many illustrative examples concerning topics which have been of especial interest to workers in the field, and by sketches of the proofs of the major results. The comprehensive bibliographies are designed to permit the interested reader to retrace the major stages in the development of the field if he wishes. Not so much a detailed textbook for plodding students, this volume, like the others in the series, is intended to lead researchers in other fields and advanced students quickly to an understanding of the 'state of the art' in this area of mathematics. As such it will serve both as a basic reference work on important areas of mathematical physics as they stand today, and as a good starting point for further, more detailed study for people new to this field
Real algebraic geometry by V. I Arnolʹd( Book )

15 editions published in 2013 in English and held by 116 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
Analysis and singularities : collected papers dedicated to academician Vladimir Igorevich Arnold on the occasion of his 70th birthday( Book )

7 editions published in 2007 in English and held by 40 WorldCat member libraries worldwide

Yesterday and long ago by V. I Arnolʹd( Book )

9 editions published between 2006 and 2010 in English and German and held by 27 WorldCat member libraries worldwide

V.I. Arnold was renowned for achievements in mathematics, and for the clarity of his writing. These essays offer a glimpse into the life and work of one of the world's outstanding mathematicians
Collected works by V. I Arnolʹd( Book )

18 editions published in 2009 in English and held by 20 WorldCat member libraries worldwide

Vladimir Arnold is one of the great 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
 
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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.

Vladímir Arnold matemàtic rus

Vladímir Arnold matemático ruso

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

ולדימיר ארנולד מתמטיקאי רוסי

فلاديمير أرنولد

فلاديمير أرنولد رياضياتي روسي

ولادیمیر آرنولد ریاضی‌دان روسی

விளாதிமிர் ஆர்னோல்டு

블라디미르 아르놀트

アーノルド, V. I.

ウラジーミル・アーノルド

弗拉基米爾·阿諾爾德

Languages
Covers
Mathematical methods of classical mechanicsCatastrophe theoryGeometrical methods in the theory of ordinary differential equationsMathematics : frontiers and perspectivesLectures on partial differential equationsMathematical aspects of classical and celestial mechanicsTopological methods in hydrodynamicsBifurcation theory and catastrophe theory