Catastrophe Theory

Couverture
Springer Science & Business Media, 6 déc. 2012 - 150 pages

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.

 

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Table des matières

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
Appendix The Precursors of Catastrophe Theory
108
Conclusion
114
Problems
119

The LargeScale Distribution of Matter in the Universe
45
the Maximum Function
49
Singularities of the Boundary of Attainability
53
References
129
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