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 .