Ebook: Catastrophe Theory

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Content:
Front Matter....Pages i-xii
Singularities, Bifurcations, and Catastrophe Theories....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 the Generation of Auto-Oscillations....Pages 20-26
Singularities of Stability Boundaries and the Principle of the Fragility of Good Things....Pages 27-28
Caustics, Wave Fronts and Their Metamorphoses....Pages 29-38
Large Scale Distribution of Matter in the Universe....Pages 39-42
Singularities in Optimization Problems, the Maxima Function....Pages 43-46
Singularities of Accessibility Boundaries....Pages 47-56
Smooth Surfaces and Their Projections....Pages 57-62
Problems of By-Passing Obstacles....Pages 63-65
Symplectic and Contact Geometries....Pages 66-74
The Mystics of Catastrophe Theory....Pages 75-78
Back Matter....Pages 79-79

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Content:
Front Matter....Pages i-xii
Singularities, Bifurcations, and Catastrophe Theories....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 the Generation of Auto-Oscillations....Pages 20-26
Singularities of Stability Boundaries and the Principle of the Fragility of Good Things....Pages 27-28
Caustics, Wave Fronts and Their Metamorphoses....Pages 29-38
Large Scale Distribution of Matter in the Universe....Pages 39-42
Singularities in Optimization Problems, the Maxima Function....Pages 43-46
Singularities of Accessibility Boundaries....Pages 47-56
Smooth Surfaces and Their Projections....Pages 57-62
Problems of By-Passing Obstacles....Pages 63-65
Symplectic and Contact Geometries....Pages 66-74
The Mystics of Catastrophe Theory....Pages 75-78
Back Matter....Pages 79-79
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