Vladimir Arnold – Collected Works

<p>1&nbsp; Modes
and Quasimodes.- 2&nbsp; Integrals of Rapidly
Oscillating Functions and Singularities of Projections of Lagrangian Manifolds.-
3&nbsp; Remarks on the Stationary Phase Method
and Coxeter Numbers.- 4&nbsp; Normal Forms of
Functions near Degenerate Critical Points, the Weyl Groups A_k, D_k,
E_k, and Lagrangian
Singularities.- 5&nbsp; Normal Forms of
Functions in Neighbourhoods of Degenerate Critical Points.- 6&nbsp; Critical Points of Functions and
Classification of Caustics.- 7&nbsp;
Classification of Unimodal Critical Points of Functions.- 8&nbsp;
Classification of Bimodal Critical Points of Functions.- 9&nbsp;
Spectral Sequence for Reduction of Functions to Normal Form.- 10&nbsp;
Spectral Sequences for Reducing Functions to Normal Forms.- 11&nbsp;
Critical Points of Smooth Functions and Their Normal Forms.- 12&nbsp; Local
Normal Forms of Functions.- 13&nbsp; Some Open Problems in Singularity Theory.- 14&nbsp; On the Theory of Envelopes.- 15&nbsp; Wave
Front Evolution and Equivariant Morse Lemma.- 16&nbsp; A Correction to: Wave Front
Evolution and Equivariant Morse Lemma.- 17&nbsp; A Conjecture on the Signature
of the Quadratic Form of a Quasihomogeneous Singularity.- 18&nbsp; On
Contemporary Developments of I.G. Petrovskii's Works on Topology of Real
Algebraic Varieties .- 19&nbsp; Topology of Real Algebraic Varieties (with O.A. Oleinik).- 20&nbsp; Bifurcations of Invariant Manifolds of
Differential Equations and Normal Forms of Neighborhoods of Elliptic Curves.- 21&nbsp; Loss of Stability of Self-Oscillations Close
to Resonances and Versal Deformations of Equivariant Vector Fields.- 22&nbsp; Some Problems in the Theory of Differential
Equations.- 23&nbsp; Bifurcations of Discrete Dynamical Systems
(with A.P. Shapiro).- 24&nbsp; Index
of a Singular Point of a Vector Field, the Petrovskii-Oleinik Inequality, and
Mixed Hodge Structures (in Russian).- 25&nbsp; Index of a Singular Point of a Vector Field,
the Petrovskii-Oleinik Inequalities, and Mixed Hodge Structures.- 26&nbsp;
Critical Points of Functions on a Manifold with Boundary, the Simple Lie
Groups B_k, C_k, and F₄, and Singularities of Evolutes.- 27&nbsp;
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&nbsp; Stable Oscillations with Potential Energy
Harmonic in Space and Periodic in Time.- 29&nbsp; The Loss of Stability of Self-Induced
Oscillations near Resonances.- 30&nbsp; Catastrophe Theory.- 31&nbsp;
Superposition of Algebraic Functions (with G. Shimura).- 32&nbsp; The A-D-E Classifications.- 33&nbsp; Real
Algebraic Geometry (the 16th Hilbert Problem).- 34&nbsp; Study of Singularities.- 35&nbsp; Dynamical Systems and Differential Equations.-
36&nbsp; Fixed Points of Symplectic
Diffeomorphisms.- 37&nbsp; Partial
Differential Equations: What Is a Mathematical Equivalent to Physical
”Turbulence“?.- 38&nbsp;
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&nbsp; A Regional Mathematical School in Syktyvkar
(with A.M. Vershik, D.B. Fuks, and Ya.M. Eliashberg) (in Russian).- 41&nbsp; Kolmogorov’s
School.- 42 Preface to the
Collection “Singularities of Differentiable Mappings” of Russian Translations
of Papers in English and French.- 43&nbsp; 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.- &nbsp;45 Preface to the Russian Translation of the
Book “Differentiable Germs and Catastrophes” by Th. Bröcker and L. Lander.- 46&nbsp;
Preface to the Russian Translation of the Book “Stable Mappings and
Their Singularities” by M. Golubitsky and V. Guillemin.</p>