Catastrophe theory
V. I. Arnol'd ; translated from the Russian by G. S. Wassermann ; based on a translation by R. K. Thomas.
3rd rev. and expanded ed.
Berlin : Springer-Verlag, ©1992.
xiii, 150 págs. : ilustraciones ; 21 cm.
ISBN: 3540548114 (Berlin), 0387548114 (New York)
Traducción de: Teoriia katastrof.
Incluye referencias bibliográficas (p. 129-150).
Reseña: MathSciNet, 93h:58018
Contenido
- 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.
