Arnolʹd, V. I. (Vladimir Igorevich) 19372010Overview
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V. I Arnolʹd
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V. I Arnolʹd
Ordinary differential equations
by V. I Arnolʹd
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57 editions published between 1973 and 2009 in English and Undetermined and held by 1,444 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 oneparameter groups of linear transformations (equivalent to the theory of linear autonomous systems). The book also develops whole congeries of fundamental conceptslike phase space and phase flows, smooth manifolds and tangent bundles, vector fields and oneparameter groups of diffeomorphismsthat remain in the shadows in the traditional coordinatebased 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
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Book
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71 editions published between 1978 and 2011 in 3 languages and held by 1,421 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
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Book
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47 editions published between 1983 and 2004 in 5 languages and held by 1,285 WorldCat member libraries worldwide "This short book, which is a translation from the original Russian, provides a concise, nonmathematical 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 nonmathematical review of catastrophe theory which will provide a useful introduction to the subject."Physics Bulletin
Singularity theory selected papers
by V. I Arnolʹd
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22 editions published between 1981 and 1993 in English and Undetermined and held by 947 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
Geometrical methods in the theory of ordinary differential equations
by V. I Arnolʹd
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Book
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29 editions published between 1982 and 2004 in English and German and held by 945 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
Mathematical aspects of classical and celestial mechanics
by V. I Arnolʹd
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47 editions published between 1988 and 2009 in English and German and held by 761 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
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Book
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27 editions published between 1899 and 2013 in English and Undetermined and held by 676 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 Kortewegde 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, grouptheoretic, 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
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27 editions published between 2004 and 2005 in English and held by 660 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
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12 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
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21 editions published between 1968 and 1989 in English and Spanish and held by 578 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
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Book
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12 editions published between 1989 and 1992 in English and Italian and held by 553 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 presentday 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
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12 editions published between 2004 and 2009 in English and German and held by 528 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 Kortewegde 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
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25 editions published between 1990 and 1993 in English and held by 501 WorldCat member libraries worldwide
Singularities of differentiable maps
by V. I Arnolʹd
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35 editions published between 1984 and 2012 in 3 languages and held by 460 WorldCat member libraries worldwide
Bifurcation theory and catastrophe theory
by V. I Arnolʹd
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Book
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33 editions published between 1991 and 2009 in English and German and held by 336 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 nonsmooth. 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
Real algebraic geometry
by V. I Arnolʹd
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9 editions published in 2013 in English and held by 324 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)
Trends and perspectives in applied mathematics
by L Sirovich
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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, HeinzOtto 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
Collected Works
by V. I Arnolʹd
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10 editions published in 2009 in English and held by 307 WorldCat member libraries worldwide
The dynamics, statistics and projective geometry of Galois fields
by V. I Arnolʹd
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Book
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13 editions published between 2010 and 2011 in English and Undetermined and held by 282 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
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3 editions published in 2012 in English and held by 276 WorldCat member libraries worldwide more
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Associated Subjects
Algebra Algebra, Homological Arnolʹd, V. I.(Vladimir Igorevich), Bifurcation theory Canada Catastrophes (Mathematics) Celestial mechanics Critical point theory (Mathematical analysis) Differentiable dynamical systems Differentiable mappings Differential algebra Differential equations Differential equations, Partial Differential equationsAsymptotic theory Differential topology Dynamics Engineering Ergodic theory Finite fields (Algebra) Fluids Galois theory Geometry Geometry, Algebraic Geometry, Differential Global analysis (Mathematics) Gödel, Kurt Hydrodynamics HydrodynamicsMathematical models John, Fritz, Klein, Felix, Leibniz, Gottfried Wilhelm,Freiherr von, Lyapunov functions Lyapunov stability Mathematical analysis Mathematical analysisFoundations Mathematical physics Mathematicians Mathematics Mechanics, Analytic Nonstandard mathematical analysis Numerical analysis Physics Russia Russia (Federation) ScienceMathematics Singularities (Mathematics) Soviet Union Stability Topology United States

Alternative Names
Arnol′d Vladimir Igorevich 19372010
Arnol′d Vladimir Igorevitch 19372010
Arnold, V.
Arnold, V. 19372010
Arnold , V. I.
Arnold, V. I., 1937
Arnold, V. I. 19372010
Arnolʹd, V. I. (Vladimir Igorevič), 19372010
Arnold, Vl., 19372010
Arnold Vladimir 19372010
Arnold, Vladimir I.
Arnolʹd, Vladimir I. 19372010
Arnolʹd, Vladimir Igorevič
Arnold, Vladimir Igorevič 19372010
Arnolʹd, Vladimir Igorevich
Arnolʹd, Vladimir Igorevich, 1937
Arnolʹd, Vladimir Igorevich, 19372010
Arnold, W. I.
Арнольд, В. И. (Владимир Игоревич), 19372010
Арнольд, Владимир Игоревич.
Арнольд, Владимир Игоревич, 19372010
アーノルド, V. I
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