Ebook: Catastrophe Theory

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Content:
Front Matter....Pages I-XIII
Singularities, Bifurcations, and Catastrophes....Pages 1-2
Whitney’s Singularity Theory....Pages 3-6
Applications of Whitney’s Theory....Pages 7-9
A Catastrophe Machine....Pages 10-13
Bifurcations of Equilibrium States....Pages 14-19
Loss of Stability of Equilibrium and of Self-Oscillating Modes of Behaviour....Pages 20-26
Singularities of the Stability Boundary and the Principle of the Fragility of Good Things....Pages 27-28
Caustics, Wave Fronts, and Their Metamorphoses....Pages 29-39
The Large-Scale Distribution of Matter in the Universe....Pages 40-43
Singularities in Optimization Problems: the Maximum Function....Pages 44-46
Singularities of the Boundary of Attainability....Pages 47-56
Smooth Surfaces and Their Projections....Pages 57-62
The Problem of Bypassing an Obstacle....Pages 63-66
Symplectic and Contact Geometry....Pages 67-75
Complex Singularities....Pages 76-88
The Mysticism of Catastrophe Theory....Pages 89-93
Back Matter....Pages 95-110

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Content:
Front Matter....Pages I-XIII
Singularities, Bifurcations, and Catastrophes....Pages 1-2
Whitney’s Singularity Theory....Pages 3-6
Applications of Whitney’s Theory....Pages 7-9
A Catastrophe Machine....Pages 10-13
Bifurcations of Equilibrium States....Pages 14-19
Loss of Stability of Equilibrium and of Self-Oscillating Modes of Behaviour....Pages 20-26
Singularities of the Stability Boundary and the Principle of the Fragility of Good Things....Pages 27-28
Caustics, Wave Fronts, and Their Metamorphoses....Pages 29-39
The Large-Scale Distribution of Matter in the Universe....Pages 40-43
Singularities in Optimization Problems: the Maximum Function....Pages 44-46
Singularities of the Boundary of Attainability....Pages 47-56
Smooth Surfaces and Their Projections....Pages 57-62
The Problem of Bypassing an Obstacle....Pages 63-66
Symplectic and Contact Geometry....Pages 67-75
Complex Singularities....Pages 76-88
The Mysticism of Catastrophe Theory....Pages 89-93
Back Matter....Pages 95-110
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