Catastrophe TheoryThe new edition of this non-mathematical review of catastrophe theory contains updated results and many new or expanded topics including delayed loss of stability, shock waves, and interior scattering. Three new sections offer the history of singularity and its applications from da Vinci to today, a discussion of perestroika in terms of the theory of metamorphosis, and a list of 93 problems touching on most of the subject matter in the book. |
Contents
| 1 | |
| 2 | |
Applications of Whitneys Theory | 3 |
A Catastrophe Machine | 10 |
Bifurcations of Equilibrium States | 14 |
Loss of Stability of Equilibrium and of SelfOscillating Modes of Behaviour | 20 |
Singularities of the Stability Boundary and the Principle of the Fragility of Good Things | 31 |
Caustics Wave Fronts and Their Metamorphoses | 33 |
31 | 53 |
Smooth Surfaces and Their Projections | 67 |
The Problem of Bypassing an Obstacle | 75 |
Symplectic and Contact Geometry | 79 |
Complex Singularities | 89 |
The Mysticism of Catastrophe Theory | 102 |
Appendix The Precursors of Catastrophe Theory | 108 |
Conclusion | 114 |
The LargeScale Distribution of Matter in the Universe | 45 |
the Maximum Function | 49 |
1 | 50 |
7 | 51 |
Problems | 119 |
References | 129 |
Other editions - View all
Common terms and phrases
Anal Appl attractor bifurcation catastrophe theory caustics and wave codimension complex contact structure convex hulls coordinates critical points critical values cusp points cusp ridge diffeomorphic dimension Dynamical Systems E. C. Zeeman English translation equation equilibrium Euclidean space example Funct Funkts Gauss mapping geodesics geometry hypersurface indicatrix inflection intersection investigation Itogi Nauki Tekh Lagrangian Legendre Let us consider level curve level manifold limiting curves loss of stability mapping Math mathematical metamorphoses monodromy Moscow Nauk neighbourhood normal form one-parameter family oscillations parameter perestroikas phase curves phase space plane Poincaré polynomials Prilozh problem projection Russ Russian Shcherbak singu singular points singularities of caustics singularity theory small perturbation smooth function smooth surfaces Sovrem sphere submanifold Surv swallowtail symplectic structure tangent theorem Thom three-dimensional space three-space tion topologically torus transformation typical singularities V. I. Arnol'd vanishing cycle variables vector field velocity VINITI visible contour wave fronts Whitney's zero