Catastrophe Theory - Brossura

Arnol'D, V. I.

Brossura

ISBN 10: 354012859X ISBN 13: 9783540128595

Casa editrice: Springer Verlag, 1984

Riassunto

Singularity theory is growing very fast and many new results have been discovered since the Russian edition appeared: for instance the relation of the icosahedron to the problem of by­ passing a generic obstacle. The reader can find more details about this in the articles "Singularities of ray systems" and "Singularities in the calculus of variations" listed in the bi­ bliography of the present edition. Moscow, September 1983 v. I. Arnold Preface to the Russian Edition "Experts discuss forecasting disasters" said a New York Times report on catastrophe theory in November 1977. The London Times declared Catastrophe Theory to be the "main intellectual movement of the century" while an article on catastrophe theory in Science was headed "The emperor has no clothes". This booklet explains what catastrophe theory is about and why it arouses such controversy. It also contains non-con­ troversial results from the mathematical theories of singulari­ ties and bifurcation. The author has tried to explain the essence of the fundamen­ tal results and applications to readers having minimal mathe­ matical background but the reader is assumed to have an in­ quiring mind. Moscow 1981 v. I. Arnold Contents Chapter 1. Singularities, Bifurcations, and Catastrophe Theories ............... 1 Chapter 2. Whitney's Singularity Theory ... 3 Chapter 3. Applications of Whitney's Theory 7 Chapter 4. A Catastrophe Machine ...... 10 Chapter 5. Bifurcations of Equilibrium States 14 Chapter 6. Loss of Stability of Equilibrium and the Generation of Auto-Oscillations . . . . . . 20 .

Su questo libro

Recensione:

"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

"Vladimir Arnold is a giant among contemporary mathematicians, and one of the three who stand out in the creation and development of catastrophe theory. ..."

The Times Higher Education Supplement 1 June 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

"This unusual little paperback ... has the qualities we tend to associate with Russian expository mathematical writing: a highly personal style, imaginatevely presented examples, nontechnical language, sometimes puzzling asides, and de trop obersations taken from the world at large. ..."

The Mathematical Intelligencer 18.1996.4

 

 

Contenuti:

1. Singularities, Bifurcations, and Catastrophe Theories.- 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 the Generation of Auto-Oscillations.- 7. Singularities of Stability Boundaries and the Principle of the Fragility of Good Things.- 8. Caustics, Wave Fronts and Their Metamorphoses.- 9. Large Scale Distribution of Matter in the Universe.- 10. Singularities in Optimization Problems, the Maxima Function.- 11. Singularities of Accessibility Boundaries.- 12. Smooth Surfaces and Their Projections.- 13. Problems of By-Passing Obstacles.- 14. Symplectic and Contact Geometries.- 15. The Mystics of the Catastrophe Theory.- References.

Su questa edizione

• Editore: Springer Verlag
• Data di pubblicazione: 1984
• ISBN 10: 354012859X
• ISBN 13: 9783540128595
• Rilegatura: Copertina flessibile
• Numero di pagine: 88