Singularity theory 1972-1979
著者
書誌事項
Singularity theory 1972-1979
（Collected works / Vladimir I. Arnold, v. 3）
Springer, c2016
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注記
Other editors: Boris A. Khesin, Mikhail B. Sevryuk, Victor A. Vassiliev, Oleg Ya. Viro
Includes bibliographical references
内容説明・目次
内容説明
Volume
III of the Collected Works of V.I. Arnold contains papers written in the years 1972 to 1979.
The main theme emerging in Arnold's work of this period is the development of
singularity theory of smooth functions and mappings.
The
volume also contains papers by V.I. Arnold on catastrophe theory and on A.N.
Kolmogorov's school, his prefaces to Russian editions of several books related
to singularity theory, V. Arnold's lectures on bifurcations of discrete
dynamical systems, as well as a review by V.I. Arnold and Ya.B. Zeldovich of
V.V. Beletsky's book on celestial mechanics.
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.
目次
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 Ak, Dk,
Ek, 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 Problems in 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-Oleinik Inequality, 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 Bk, Ck, and F4, 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 a l'etude topologique des singularites 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. Broecker and L. Lander.- 46
Preface to the Russian Translation of the Book "Stable Mappings and
Their Singularities" by M. Golubitsky and V. Guillemin.
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