## 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. |

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### Contents

Singularities Bifurcations and Catastrophes | 1 |

Whitneys Singularity Theory | 3 |

Applications of Whitneys Theory | 7 |

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 |

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 |

The Precursors of Catastrophe Theory | 108 |

Conclusion | 114 |

Problems | 119 |

The LargeScale Distribution of Matter in the Universe | 45 |

Singularities in Optimization Problems the Maximum Function | 49 |

Singularities of the Boundary of Attainability | 53 |

References | 129 |

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### Common terms and phrases

Anal asymptotic lines attainability domain attractor axis behaviour bifurcation big caustic called catastrophe theory caustics and wave codimension contact structure convex hulls coordinates corresponding critical points critical values cusp points cusp ridge cusp singularities cylinder described diffeomorphic dimension ellipse English translation equation equilibrium Euclidean space example fibration folds and cusps Gauss mapping geodesics geometry hypersurface indicatrix inflection intersect investigation involutes jump Legendre Let us consider level curve level manifold limiting curves loss of stability Math mathematical medium metamorphoses monodromy neighbourhood node nonsingular obstacle surface one-parameter family original oscillations parameter perestroikas phase curves phase space polynomials problem projection Prove segment simplest singu singular points singularities of caustics singularity theory small perturbation smooth change smooth function smooth surface space-time sphere submanifold swallowtail symplectic structure tangent theorem Thom three-dimensional space three-space tion topologically torus transformation typical singularities V. I. Arnol'd vanishing cycle vector field visible contour wave fronts Whitney Whitney's zero