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Full Description
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.
Contents
1 Statistics of integral convex polygons.- 2 On some problems in singularity theory.- 3 On some nonlinear problems.- 4 The problems proposed at the Second International Conference of alumni of Moscow State University (Faculty of Mechanics and Mathematics) on the topic "Differential Equations and Their Applications".- 5 Lagrange and Legendre cobordisms. I.- 6 Lagrange and Legendre cobordisms. II.- 7 Sweeping a caustic by a caspidal edge of a moving front.- 8 Singularities of Legendre varieties, of evolvents and of fronts at an obstacle.- 9 Elements of the large-scale structure of the universe (with Ya.B. Zeldovich and S.F. Shandarin).- 10 The large-scale structure of the Universe. I. General properties. One- and two-dimensional models (with S.F. Shandarin and Ya.B. Zeldovich).- 11 Evolution of singularities of potential flows in collision-free media and the metamorphosis of caustics in three-dimensional space.- 12 On the Newtonian potential of hyperbolic layers.- 13 On the Newtonian attraction of clusters of dust-like particles.- 14 Some algebro-geometrical aspects of the Newton attraction theory.- 15 Magnetic analogues of Newton's and Ivory's theorems.- 16 Some remarks on elliptic coordinates.- 17 Lagrangian manifolds with singularities, asymptotic rays, and the open swallowtail.- 18 Asymptotic rays in symplectic geometry (in Russian).- 19 Singularities of systems of rays.- 20 Singularities of ray systems.- 21 Singularities in variational calculus.- 22 Singularities in variational calculus.- 23 Singularities, bifurcations, and catastrophes.- 24 Singularities of functions, wave fronts, caustics and multidimensional integrals (with A.N. Varchenko, A.B. Givental, and A.G. Khovanskii).- 25 Remarks on the perturbation theory for problems of Mathieu type.- 26 Vanishing inflections.- 27 Appendix A to the paper: B.A. Malomed and M.I. Tribelsky "Bifurcations in distributed kinetic systems with aperiodic instability".- 28 Reversible systems.- 29 Oscillations and bifurcations in reversible systems (with M.B. Sevryuk).- 30 The period map and Poisson structures.- 31 Frontier problems.- 32 Preface to the book "Selected Works by Hermann Weyl" (with A.N. Parshin).- 33 Comments to the paper "Das asymptotische Verteilungsgesetz der Eigenschwingungen eines beliebig gestalteten elastischen Körpers" by Hermann Weyl (with A.N. Parshin).- 34 Comments to the paper "On the volume of tubes" by Hermann Weyl.- 35 Classical mechanics.- 36 Superpositions.
