V. I. Arnolʹd Libri

This book presents a modern approach to classical mechanics, starting from fundamental concepts in dynamics. It emphasizes geometric considerations, exploring phase spaces, vector fields, and Lie groups. The author also discusses qualitative methods in dynamical systems and asymptotic techniques, offering a fresh perspective compared to traditional texts.

From the reviews: "... As an encyclopaedia article, this book does not seek to serve as a textbook, nor to replace the original articles whose results it describes. The book's goal is to provide an overview, pointing out highlights and unsolved problems, and putting individual results into a coherent context. It is full of historical nuggets, many of them surprising. ... The examples are especially helpful; if a particular topic seems difficult, a later example frequently tames it. The writing is refreshingly direct, never degenerating into a vocabulary lesson for its own sake. The book accomplishes the goals it has set for itself. While it is not an introduction to the field, it is an excellent overview. ..." American Mathematical Monthly, Nov. 1989 "This is a book to curl up with in front of a fire on a cold winter's evening. ..." SIAM Reviews, Sept. 1989

Choice Outstanding Title! (January 2006)This richly illustrated text covers the Cauchy and Neumann problems for the classical linear equations of mathematical physics. 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. No other mathematical writer does this quite so well as Arnold.

The first two chapters of this book have been thoroughly revised and sig nificantly expanded. Sections have been added on elementary methods of in tegration (on homogeneous and inhomogeneous first-order linear equations and on homogeneous and quasi-homogeneous equations), on first-order linear and quasi-linear partial differential equations, on equations not solved for the derivative, and on Sturm's theorems on the zeros of second-order linear equa tions. Thus the new edition contains all the questions of the current syllabus in the theory of ordinary differential equations. In discussing special devices for integration the author has tried through out to lay bare the geometric essence of the methods being studied and to show how these methods work in applications, especially in mechanics. Thus to solve an inhomogeneous linear equation we introduce the delta-function and calculate the retarded Green's function; quasi-homogeneous equations lead to the theory of similarity and the law of universal gravitation, while the theorem on differentiability of the solution with respect to the initial conditions leads to the study of the relative motion of celestial bodies in neighboring orbits. The author has permitted himself to include some historical digressions in this preface. Differential equations were invented by Newton (1642-1727).

This is a charming collection of essays on life and science, by one of the leading mathematicians of our day. Vladimir Igorevich Arnold is renowned for his achievements in mathematics, and nearly as famous for his informal teaching style, and for the clarity and accessibility of his writing. The chapter headings convey Arnold’s humor and restless imagination. A few My first recollections; The combinatorics of Plutarch; The topology of surfaces according to Alexander of Macedon; Catching a pike in Cambridge. Yesterday and Long Ago offers a rare opportunity to appreciate the life and work of one of the world’s outstanding living mathematicians.

The first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures. The book is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry.

This volume is a celebration of the state of mathematics at the end of the millennium. Produced under the auspices of the International Mathematical Union (IMU), the book was born as part of the activities of World Mathematical Year 2000. It consists of 28 articles written by influential mathematicians. Authors of 14 contributions were recognized in various years by the IMU as recipients of the Fields Medal, from K.F. Roth (Fields Medalist, 1958) to W.T. Gowers (Fields Medalist, 1998).

Focusing on the period from 1991 to 1995, this collection features 27 influential papers by renowned mathematician V.I. Arnold. His work explores a diverse range of topics, including Vassiliev's theory of invariants and knots, bifurcations of plane curves, and the combinatorial properties of Bernoulli, Euler, and Springer numbers. Additionally, Arnold delves into the geometry of wave fronts, the Berry phase, and the quantum Hall effect, showcasing his profound contributions to modern mathematics.

Volume IV of the Collected Works of V.I. Arnold includes papers written mostly during the period from 1980 to 1985. Arnold’s work of this period is so multifaceted that it is almost impossible to give a single unifying theme for it. It ranges from properties of integral convex polygons to the large-scale structure of the Universe. Also during this period Arnold wrote eight papers related to magnetic dynamo problems, which were included in Volume II, mostly devoted to hydrodynamics. Thus the topic of singularities in symplectic and contact geometry was chosen only as a “marker” for this volume. There are many articles specifically translated for this volume. They include problems for the Moscow State University alumni conference, papers on magnetic analogues of Newton’s and Ivory’s theorems, on attraction of dust-like particles, on singularities in variational calculus, on Poisson structures, and others. The volume also contains translations of Arnold’s comments to Selected works of H. Weyl and those of A.N. Kolmogorov. Vladimir Arnold was 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.

The main theme emerging in Arnold's work of this period is the development ofsingularity theory of smooth functions and mappings.Thevolume also contains papers by V.I. Arnold's lectures on bifurcations of discretedynamical systems, as well as a review by V.I.