Vladimir Arnold - Collected Works

1 Modes and Quasimodes.- 2 Integrals of Rapidly Oscillating Functions and Singularities of Projections of Lagrangian Manifolds.- 3 Remarks on the Stationary Phase Method and Coxeter Numbers.- 4 Normal Forms of Functions near Degenerate Critical Points, the Weyl Groups A_k , D_k , E_k , and Lagrangian Singularities.- 5 Normal Forms of Functions in Neighbourhoods of Degenerate Critical Points.- 6 Critical Points of Functions and Classification of Caustics.- 7 Classification of Unimodal Critical Points of Functions.- 8 Classification of Bimodal Critical Points of Functions.- 9 Spectral Sequence for Reduction of Functions to Normal Form.- 10 Spectral Sequences for Reducing Functions to Normal Forms.- 11 Critical Points of Smooth Functions and Their Normal Forms.- 12 Local Normal Forms of Functions.- 13 Some Open Problemsin Singularity Theory.- 14 On the Theory of Envelopes.- 15 Wave Front Evolution and Equivariant Morse Lemma.- 16 A Correction to: Wave Front Evolution and Equivariant Morse Lemma.- 17 A Conjecture on the Signature of the Quadratic Form of a Quasihomogeneous Singularity.- 18 On Contemporary Developments of I.G. Petrovskii's Works on Topology of Real Algebraic Varieties .- 19 Topology of Real Algebraic Varieties (with O.A. Oleinik).- 20 Bifurcations of Invariant Manifolds of Differential Equations and Normal Forms of Neighborhoods of Elliptic Curves.- 21 Loss of Stability of Self-Oscillations Close to Resonances and Versal Deformations of Equivariant Vector Fields.- 22 Some Problems in the Theory of Differential Equations.- 23 Bifurcations of Discrete Dynamical Systems (with A.P. Shapiro).- 24 Index of a Singular Point of a Vector Field, the Petrovskii-OleinikInequality, and Mixed Hodge Structures (in Russian).- 25 Index of a Singular Point of a Vector Field, the Petrovskii-Oleinik Inequalities, and Mixed Hodge Structures.- 26 Critical Points of Functions on a Manifold with Boundary, the Simple Lie Groups B_k , C_k , and F ₄, and Singularities of Evolutes.- 27 Indices of Singular Points of 1-Forms on a Manifold with Boundary, Convolution of Invariants of Reflection Groups, and Singular Projections of Smooth Surfaces.- 28 Stable Oscillations with Potential Energy Harmonic in Space and Periodic in Time.- 29 The Loss of Stability of Self-Induced Oscillations near Resonances.- 30 Catastrophe Theory.- 31 Superposition of Algebraic Functions (with G. Shimura).- 32 The A-D-E Classifications.- 33 Real Algebraic Geometry (the 16th Hilbert Problem).- 34 Study of Singularities.- 35 Dynamical Systems and Differential Equations.- 36 Fixed Points of Symplectic Diffeomorphisms.- 37 Partial Differential Equations: What Is a Mathematical Equivalent to Physical "Turbulence"?.- 38 The Beginning of a New Style in the Scientific Literature (a Review of V.V. Beletsky's Book "Essays on the Motion of Celestial Bodies", Moscow: Nauka Publishing House, 1972) (with Ya.B. Zeldovich).- 39 On the First All-Union Mathematical Student Olympiad (with A.A. Kirillov, V.M. Tikhomirov, and M.A. Shubin).- 40 A Regional Mathematical School in Syktyvkar (with A.M. Vershik, D.B. Fuks, and Ya.M. Eliashberg) (in Russian).- 41 Kolmogorov's School.- 42 Preface to the Collection "Singularities of Differentiable Mappings" of Russian Translations of Papers in English and French.- 43 Preface to the Russian Translation of the Book "Introduction à l'étude topologique des singularités de Landau" by F. Pham.- 44 Preface to the Russian Translation of the Book "Singular Points of Complex Hypersurfaces" by J. Milnor.- 45 Preface to the Russian Translation of the Book "Differentiable Germs and Catastrophes" by Th. Bröcker and L. Lander.- 46 Preface to the Russian Translation of the Book "Stable Mappings and Their Singularities" by M. Golubitsky and V. Guillemin.