The 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.
|Publisher:||Springer Berlin Heidelberg|
|Edition description:||3rd, rev. and exp. ed. 1992. 2nd printing 2003|
|Product dimensions:||5.24(w) x 7.99(h) x 0.02(d)|
Table of Contents1 Singularities, Bifurcations, and Catastrophes.- 2 Whitney’s Singularity Theory.- 3 Applications of Whitney’s Theory.- 4 A Catastrophe Machine.- 5 Bifurcations of Equilibrium States.- 6 Loss of Stability of Equilibrium and of Self-Oscillating Modes of Behaviour.- 7 Singularities of the Stability Boundary and the Principle of the Fragility of Good Things.- 8 Caustics, Wave Fronts, and Their Metamorphoses.- 9 The Large-Scale Distribution of Matter in the Universe.- 10 Singularities in Optimization Problems: the Maximum function.- 11 Singularities of the Boundary of Attainability.- 12 Smooth Surfaces and Their Projections.- 13 The Problem of Bypassing an Obstacle.- 14 Symplectic and Contact Geometry.- 15 Complex Singularities.- 16 The Mysticism of Catastrophe Theory.- Appendix The Precursors of Catastrophe Theory.- Conclusion.- Problems.- References.