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. This second volume of his Collected Works focuses on hydrodynamics, bifurcation theory, and algebraic geometry.

Volume III of the Collected Works of V.I. Arnold contains papers written in the years 1972 to 1979. The main theme emerging in Arnold's work of this period is the development of singularity theory of smooth functions and mappings. The volume also contains papers by V.I. Arnold on catastrophe theory and on A.N. Kolmogorov's school, his prefaces to Russian editions of several books related to singularity theory, V. Arnold's lectures on bifurcations of discrete dynamical systems, as well as a review by V.I. Arnold and Ya.B. Zeldovich of V.V. Beletsky's book on celestial mechanics. 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.

Volume III of the Collected Works of V.I. Arnold contains papers written in the years 1972 to 1979. The main theme emerging in Arnold's work of this period is the development of singularity theory of smooth functions and mappings. The volume also contains papers by V.I. Arnold on catastrophe theory and on A.N. Kolmogorov's school, his prefaces to Russian editions of several books related to singularity theory, V. Arnold's lectures on bifurcations of discrete dynamical systems, as well as a review by V.I. Arnold and Ya.B. Zeldovich of V.V. Beletsky's book on celestial mechanics. 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.

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. This second volume of his Collected Works focuses on hydrodynamics, bifurcation theory, and algebraic geometry.

Vladimir Igorevich Arnold is one of the most influential mathematicians of our time. V. I. Arnold launched several mathematical domains (such as modern geometric mechanics, symplectic topology, and topological fluid dynamics) and contributed, in a fundamental way, to the foundations and methods in many subjects, from ordinary differential equations and celestial mechanics to singularity theory and real algebraic geometry. Even a quick look at a partial list of notions named after Arnold already gives an overview of the variety of such theories and domains: KAM (Kolmogorov-Arnold-Moser) theory, The Arnold conjectures in symplectic topology, The Hilbert-Arnold problem for the number of zeros of abelian integrals, Arnold's inequality, comparison, and complexification method in real algebraic geometry, Arnold-Kolmogorov solution of Hilbert's 13th problem, Arnold's spectral sequence in singularity theory, Arnold diffusion, The Euler-Poincare-Arnold equations for geodesics on Lie groups, Arnold's stability criterion in hydrodynamics, ABC (Arnold-Beltrami-Childress) ?ows in ?uid dynamics, The Arnold-Korkina dynamo, Arnold's cat map, The Arnold-Liouville theorem in integrable systems, Arnold's continued fractions, Arnold's interpretation of the Maslov index, Arnold's relation in cohomology of braid groups, Arnold tongues in bifurcation theory, The Jordan-Arnold normal forms for families of matrices, The Arnold invariants of plane curves. Arnold wrote some 700 papers, and many books, including 10 university textbooks. He is known for his lucid writing style, which combines mathematical rigour with physical and geometric intuition. Arnold's books on Ordinarydifferentialequations and Mathematical methodsofclassicalmechanics became mathematical bestsellers and integral parts of the mathematical education of students throughout the world."

Vladimir Igorevich Arnold is one of the most influential mathematicians of our time. V. I. Arnold launched several mathematical domains (such as modern geometric mechanics, symplectic topology, and topological fluid dynamics) and contributed, in a fundamental way, to the foundations and methods in many subjects, from ordinary differential equations and celestial mechanics to singularity theory and real algebraic geometry. Even a quick look at a partial list of notions named after Arnold already gives an overview of the variety of such theories and domains: KAM (Kolmogorov-Arnold-Moser) theory, The Arnold conjectures in symplectic topology, The Hilbert-Arnold problem for the number of zeros of abelian integrals, Arnold's inequality, comparison, and complexification method in real algebraic geometry, Arnold-Kolmogorov solution of Hilbert's 13th problem, Arnold's spectral sequence in singularity theory, Arnold diffusion, The Euler-Poincare-Arnold equations for geodesics on Lie groups, Arnold's stability criterion in hydrodynamics, ABC (Arnold-Beltrami-Childress) ?ows in ?uid dynamics, The Arnold-Korkina dynamo, Arnold's cat map, The Arnold-Liouville theorem in integrable systems, Arnold's continued fractions, Arnold's interpretation of the Maslov index, Arnold's relation in cohomology of braid groups, Arnold tongues in bifurcation theory, The Jordan-Arnold normal forms for families of matrices, The Arnold invariants of plane curves. Arnold wrote some 700 papers, and many books, including 10 university textbooks. He is known for his lucid writing style, which combines mathematical rigour with physical and geometric intuition. Arnold's books on Ordinarydifferentialequations and Mathematical methodsofclassicalmechanics became mathematical bestsellers and integral parts of the mathematical education of students throughout the world.

This volume 6 of the Collected Works comprises 27 papers by V.I.Arnold, one of the most outstanding mathematicians of all times, written in 1991 to 1995. During this period Arnold's interests covered Vassiliev's theory of invariants and knots, invariants and bifurcations of plane curves, combinatorics of Bernoulli, Euler and Springer numbers, geometry of wave fronts, the Berry phase and quantum Hall effect. The articles include a list of problems in dynamical systems, a discussion of the problem of (in)solvability of equations, papers on symplectic geometry of caustics and contact geometry of wave fronts, comments on problems of A.D.Sakharov, as well as a rather unusual paper on projective topology. The interested reader will certainly enjoy Arnold's 1994 paper on mathematical problems in physics with the opening by-now famous phrase "Mathematics is the name for those domains of theoretical physics that are temporarily unfashionable." The book will be of interest to the wide audience from college students to professionals in mathematics or physics and in the history of science. The volume also includes translations of two interviews given by Arnold to the French and Spanish media. One can see how worried he was about the fate of Russian and world mathematics and science in general.

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.