国外数学名著系列(续一)(影印版):动力系统[ 奇异理论II:应用 VⅢ]

Singularity Theory II Classification and ApplicationsV.I Arnol’d，V.V Goryunov，O.V Lyashko，V.A Vasil’evTranslated from the Russian by J.S JoelContentsForewordChapter 1. Classification of Functions and Mappings 81. Functions on a Manifold with Boundary 81.1. Classification of Functions on a Manifold with a Smooth Boundary 81.2. Versal Deformations and Bifurcation Diagrams 111.3. Relative Homology Basis 141.4. Intersection Form 141.5. Duality of Boundary Singularities 171.6. Functions on a Manifold with a Singular Boundary 172. Complete Intersections 202.1. Start of the Classification 212.2. Critical and Discriminant Sets 242.3. The Nonsingular Fiber 262.4. Relations Between the Tyurina and Milnor Numbers 282.5. Adding a Power of a New Variable 292.6. Relative Monodromy 292.7. Dynkin Diagrams 302.8. Parabolic and Hyperbolic Singularities 312.9. Vector Fields on a Quasihomogeneous Complete Intersection 332.10. The Space of a Miniversal Deformation of a Quasihomogeneous Singularity 352.11. Topological Triviality of Versal Deformations 363. Projections and Left-Right Equivalence 373.1. Projections of Space Curves onto the Plane 383.2. Singularities of Projections of Surfaces onto the Plane 393.3. Projections of Complete Intersections 433.4. Projections onto the Line 473.5. Mappings of the Line into the Plane 573.6. Mappings of the Plane into Three-Space 594. Nonisolated Singularities of Functions 654.1. Transversal Type of a Singularity 654.3. Topology of the Nonsingular Fiber 664.4. Series of Isolated Singularities 674.5. The Number of Indices of a Series 684.6. Functions with a One-Dimensional Complete Intersection as Critical Set and with Transversal Type Ai 695. Vector Fields Tangent to Bifurcation Varieties 795.1. Functions on Smooth Manifolds 795.2. Projections onto the Line 815.3. Isolated Singularities of Complete Intersections 825.4. The Equation of a Free Divisor 846. Divergent and Cyclic Diagrams of Mappings 846.1. Germs of Smooth Functions 856.2. Envelopes 856.3. Holopmorphic Diagrams 87Chapter 2. Applications of the Classification of Critical Points of Functions 881. Legendre Singularities 881.1. Equidistants 891.2. Projective Duality 901.3. Legendre Transformation 901.4. Singularities of Pedals and Primitives 911.5. The Higher-Dimensional Case 912. Lagrangian Singularities 922.1. Caustics 922.2. The Manifold of Centers 932.3. Caustics of Systems of Rays 942.4. The Gauss Map 952.5. Caustics of Potential Systems of Noninteracting Particles 952.6. Coexistence of Singularities 973. Singularities of Maxwell Sets 983.1. Maxwell Sets 983.2. Metamorphoses of Maxwell Sets 1003.3. Extended Maxwell Sets 1033.4. Complete Maxwell Set Close to the Singularity As 1063.5. The Structure of Maxwell Sets Close to the Metamorphosis As 1103.6. Enumeration of the Connected Components of Spaces of Nondegenerate Polynomials 1124. Bifurcations of Singular Points of Gradient Dynamical Systems 1134.1. Thom’s Conjecture 1144.2. Singularities of Corank One 1154.3. Guckenheimer’s Counterexample 1164.4. Three-Parameter Families of Gradients 1174.5. Normal Forms of Gradient Systems D4 1184.6. Bifurcation Diagrams and Phase Portaits of Standard Families 1184.7. Multiparameter Families 120Chapter 3. Singularities of the Boundaries of Domains of Function Spaces 1211. Boundary of Stability 1221.1. Domains of Stability 1221.2. Singularities of the Boundary of Stability in Low-Dimensional Spaces 1221.3. Stabilization Theorem 1231.4. Finiteness Theorem 1242. Boundary of Ellipticity 1242.1. Domains of Ellipticity 1242.2. Stabilization Theorems 1242.3. Boundaries of Ellipticity and Minimum Functions 1252.4. Singularities of the Boundary of Ellipticity in Low-Dimensional Spaces 1263. Boundary of Hyperbolicity 1273.1. Domain of Hyperbolicity 1273.2. Stabilization Theorems 1273.3. Local Hyperbolicity 1283.4. Local Properties of Domains of Hyperbolicity 1294. Boundary of the Domain of Fundamental Systems 1314.1. Domain of Fundamental Systems and the Bifurcation Set 1314.2. Singularities of Bifurcation Sets ofGeneric Three-Parameter Families 1324.3. Bifurcation Sets and Schubert Cells 1364.4. Normal Forms 1404.5. Duality 1414.6. Bifurcation Sets and Tangential Singularities 1424.7. The Group of Transformations of Sets and Finite Determinacy. 1434.8. Bifurcation Diagrams of Flattenings of Projective Curves 145S 5. Linear Differential Equations and Complete Flag Manifolds 146Chapter 4. Applications of Ramified Integrals and Generalized Picard-Lefschetz Theories 1491. Newton’s Theorem on Nonintegrability 1501.1. Newton’s Theorem and Ar