VolumeIII 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 ofsingularity theory of smooth functions and mappings. Thevolume 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 relatedto singularity theory, V. Arnold's lectures on bifurcations of discretedynamical systems, as well as a review by V.I. Arnold and Ya.B. Zeldovich ofV.V. Beletsky's book on celestial mechanics. Vladimir Arnold…mehr
VolumeIII 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 ofsingularity theory of smooth functions and mappings.
Thevolume 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 relatedto singularity theory, V. Arnold's lectures on bifurcations of discretedynamical systems, as well as a review by V.I. Arnold and Ya.B. Zeldovich ofV.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.
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.
Inhaltsangabe
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 Problemsin 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-OleinikInequality, 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 Indices of Singular Points of 1-Forms on a Manifold with Boundary,Convolution of Invariants of Reflection Groups, and Singular Projections ofSmooth Surfaces.- 28 Stable Oscillations with Potential EnergyHarmonic in Space and Periodic in Time.- 29 The Loss of Stability of Self-InducedOscillations near Resonances.- 30 Catastrophe Theory.- 31 Superposition of Algebraic Functions (with G. Shimura).- 32 The A-D-E Classifications.- 33 RealAlgebraic Geometry (the 16th Hilbert Problem).- 34 Study of Singularities.- 35 Dynamical Systems and Differential Equations.-36 Fixed Points of SymplecticDiffeomorphisms.- 37 PartialDifferential Equations: What Is a Mathematical Equivalent to Physical"Turbulence"?.- 38 The Beginning of a New Style in the Scientific Literature (a Review ofV.V. Beletsky's Book "Essays on the Motion of Celestial Bodies",Moscow: Nauka Publishing House, 1972) (with Ya.B. Zeldovich).- 39 Onthe 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'sSchool.- 42 Preface to theCollection "Singularities of Differentiable Mappings" of Russian Translationsof Papers in English and French.- 43 Preface to the Russian Translation of theBook "Introduction à l'étude topologique des singularités de Landau" by F. Pham.- 44 Preface to the Russian Translation of the Book "Singular Points ofComplex Hypersurfaces" by J. Milnor.- 45 Preface to the Russian Translation of theBook "Differentiable Germs and Catastrophes" by Th. Bröcker and L. Lander.- 46 Preface to the Russian Translation of the Book "Stable Mappings andTheir Singularities" by M. Golubitsky and V. Guillemin.
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 Problemsin 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-OleinikInequality, 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 Indices of Singular Points of 1-Forms on a Manifold with Boundary,Convolution of Invariants of Reflection Groups, and Singular Projections ofSmooth Surfaces.- 28 Stable Oscillations with Potential EnergyHarmonic in Space and Periodic in Time.- 29 The Loss of Stability of Self-InducedOscillations near Resonances.- 30 Catastrophe Theory.- 31 Superposition of Algebraic Functions (with G. Shimura).- 32 The A-D-E Classifications.- 33 RealAlgebraic Geometry (the 16th Hilbert Problem).- 34 Study of Singularities.- 35 Dynamical Systems and Differential Equations.-36 Fixed Points of SymplecticDiffeomorphisms.- 37 PartialDifferential Equations: What Is a Mathematical Equivalent to Physical"Turbulence"?.- 38 The Beginning of a New Style in the Scientific Literature (a Review ofV.V. Beletsky's Book "Essays on the Motion of Celestial Bodies",Moscow: Nauka Publishing House, 1972) (with Ya.B. Zeldovich).- 39 Onthe 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'sSchool.- 42 Preface to theCollection "Singularities of Differentiable Mappings" of Russian Translationsof Papers in English and French.- 43 Preface to the Russian Translation of theBook "Introduction à l'étude topologique des singularités de Landau" by F. Pham.- 44 Preface to the Russian Translation of the Book "Singular Points ofComplex Hypersurfaces" by J. Milnor.- 45 Preface to the Russian Translation of theBook "Differentiable Germs and Catastrophes" by Th. Bröcker and L. Lander.- 46 Preface to the Russian Translation of the Book "Stable Mappings andTheir Singularities" by M. Golubitsky and V. Guillemin.
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