Ebook: Catastrophe Theory

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 with chapters on the applications of the theory to topics such as wavefront propagation, the distribution of matter within the universe, and optimisation and control. The presentation is enhanced by numerous diagrams.

... This is a short, critical and non-mathematical review of catastrophe theory which will provide a useful introduction to the subject."

Physics Bulletin December 1984

"... This is a beautiful little book, popular mathematics at its best, a delight to read and unreservedly recommended to novice and expert alike. ..."

Acta Applicandae Mathematicae Vol. 7, 1986

"... The book can be warmly recommended to everyone who is interested in singularity theory. It also gives interesting information for researchers working on the subject."

Acta Scientiarum Mathematicarum 59, 1994

"... There is probably no one else in the world who could have written this book. It remains an engrossing summary of a vast body of work which is one of the major achievements of twentieth-century mathematics."

Mathematical Reviews, Issue 93h

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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 with chapters on the applications of the theory to topics such as wavefront propagation, the distribution of matter within the universe, and optimisation and control. The presentation is enhanced by numerous diagrams.

... This is a short, critical and non-mathematical review of catastrophe theory which will provide a useful introduction to the subject."

Physics Bulletin December 1984

"... This is a beautiful little book, popular mathematics at its best, a delight to read and unreservedly recommended to novice and expert alike. ..."

Acta Applicandae Mathematicae Vol. 7, 1986

"... The book can be warmly recommended to everyone who is interested in singularity theory. It also gives interesting information for researchers working on the subject."

Acta Scientiarum Mathematicarum 59, 1994

"... There is probably no one else in the world who could have written this book. It remains an engrossing summary of a vast body of work which is one of the major achievements of twentieth-century mathematics."

Mathematical Reviews, Issue 93h

 

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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 with chapters on the applications of the theory to topics such as wavefront propagation, the distribution of matter within the universe, and optimisation and control. The presentation is enhanced by numerous diagrams.

... This is a short, critical and non-mathematical review of catastrophe theory which will provide a useful introduction to the subject."

Physics Bulletin December 1984

"... This is a beautiful little book, popular mathematics at its best, a delight to read and unreservedly recommended to novice and expert alike. ..."

Acta Applicandae Mathematicae Vol. 7, 1986

"... The book can be warmly recommended to everyone who is interested in singularity theory. It also gives interesting information for researchers working on the subject."

Acta Scientiarum Mathematicarum 59, 1994

"... There is probably no one else in the world who could have written this book. It remains an engrossing summary of a vast body of work which is one of the major achievements of twentieth-century mathematics."

Mathematical Reviews, Issue 93h

 

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 20-30
Singularities of the Stability Boundary and the Principle of the Fragility of Good Things....Pages 31-32
Caustics, Wave Fronts, and Their Metamorphoses....Pages 33-44
The Large-Scale Distribution of Matter in the Universe....Pages 45-48
Singularities in Optimization Problems: the Maximum Function....Pages 49-52
Singularities of the Boundary of Attainability....Pages 53-66
Smooth Surfaces and Their Projections....Pages 67-74
The Problem of Bypassing an Obstacle....Pages 75-78
Symplectic and Contact Geometry....Pages 79-88
Complex Singularities....Pages 89-101
The Mysticism of Catastrophe Theory....Pages 102-107
Back Matter....Pages 108-150

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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 with chapters on the applications of the theory to topics such as wavefront propagation, the distribution of matter within the universe, and optimisation and control. The presentation is enhanced by numerous diagrams.

... This is a short, critical and non-mathematical review of catastrophe theory which will provide a useful introduction to the subject."

Physics Bulletin December 1984

"... This is a beautiful little book, popular mathematics at its best, a delight to read and unreservedly recommended to novice and expert alike. ..."

Acta Applicandae Mathematicae Vol. 7, 1986

"... The book can be warmly recommended to everyone who is interested in singularity theory. It also gives interesting information for researchers working on the subject."

Acta Scientiarum Mathematicarum 59, 1994

"... There is probably no one else in the world who could have written this book. It remains an engrossing summary of a vast body of work which is one of the major achievements of twentieth-century mathematics."

Mathematical Reviews, Issue 93h

 

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 20-30
Singularities of the Stability Boundary and the Principle of the Fragility of Good Things....Pages 31-32
Caustics, Wave Fronts, and Their Metamorphoses....Pages 33-44
The Large-Scale Distribution of Matter in the Universe....Pages 45-48
Singularities in Optimization Problems: the Maximum Function....Pages 49-52
Singularities of the Boundary of Attainability....Pages 53-66
Smooth Surfaces and Their Projections....Pages 67-74
The Problem of Bypassing an Obstacle....Pages 75-78
Symplectic and Contact Geometry....Pages 79-88
Complex Singularities....Pages 89-101
The Mysticism of Catastrophe Theory....Pages 102-107
Back Matter....Pages 108-150
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