Catastrophe Theory / by Vladimir I. Arnold.
From The Reviews: "This short book, which is a translation from the Russian, provides a concise, non-mathematical review of the less controversial results in catastrophe theory. The author begins by describing the established results in the theory of singularities and bifurcation and continues...
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| Online Access: |
Full Text (via Springer) |
|---|---|
| Main Author: | |
| Other title: | To the Memory of M.A. Leontovich. |
| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg :
Springer Berlin Heidelberg,
1992.
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| Edition: | Third, rev. and Expanded edition. |
| Subjects: |
Table of Contents:
- 1 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.