Vladimir Arnold - Collected Works

1  Modesand Quasimodes.- 2  Integrals of RapidlyOscillating Functions and Singularities of Projections of Lagrangian Manifolds.-3  Remarks on the Stationary Phase Methodand Coxeter Numbers.- 4  Normal Forms ofFunctions near Degenerate Critical Points, the Weyl Groups Ak, Dk,Ek, and LagrangianSingularities.- 5  Normal Forms ofFunctions in Neighbourhoods of Degenerate Critical Points.- 6  Critical Points of Functions andClassification 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  LocalNormal Forms of Functions.- 13  Some Open Problems in Singularity Theory.- 14  On the Theory of Envelopes.- 15  WaveFront Evolution and Equivariant Morse Lemma.- 16  A Correction to: Wave FrontEvolution and Equivariant Morse Lemma.- 17  A Conjecture on the Signatureof the Quadratic Form of a Quasihomogeneous Singularity.- 18  OnContemporary Developments of I.G. Petrovskii's Works on Topology of RealAlgebraic Varieties .- 19  Topology of Real Algebraic Varieties (with O.A. Oleinik).- 20  Bifurcations of Invariant Manifolds ofDifferential Equations and Normal Forms of Neighborhoods of Elliptic Curves.- 21  Loss of Stability of Self-Oscillations Closeto Resonances and Versal Deformations of Equivariant Vector Fields.- 22  Some Problems in the Theory of DifferentialEquations.- 23  Bifurcations of Discrete Dynamical Systems(with A.P. Shapiro).- 24  Indexof a Singular Point of a Vector Field, the Petrovskii-Oleinik Inequality, andMixed 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 LieGroups Bk, Ck, and F4, and Singularities of Evolutes.- 27

Vladimir Arnold was one of the great mathematicalscientists of our time. He is famous for both the breadth and the depth ofhis work. At the same time he is one of the most prolific and outstandingmathematical authors.