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Catastrophe Theory
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Item specifics
- Condition
- ISBN
- 9783540548119
About this product
Product Identifiers
Publisher
Springer Berlin / Heidelberg
ISBN-10
3540548114
ISBN-13
9783540548119
eBay Product ID (ePID)
4433184
Product Key Features
Number of Pages
Xiii, 150 Pages
Language
English
Publication Name
Catastrophe Theory : to the Memory of M. A. Leontovich
Publication Year
1992
Subject
Geometry / Differential, Topology, Physics / Mathematical & Computational, Mathematical Analysis
Features
Revised
Type
Textbook
Subject Area
Mathematics, Science
Format
Trade Paperback
Dimensions
Item Weight
9.3 Oz
Item Length
8 in
Item Width
5.2 in
Additional Product Features
Edition Number
3
Intended Audience
Scholarly & Professional
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"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 , "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 , "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, "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 Intelligencer18.1996.4
Number of Volumes
1 vol.
Illustrated
Yes
Edition Description
Revised edition
Table Of Content
1 Singularities, Bifurcations, and Catastrophes.- 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 of Self-Oscillating Modes of Behaviour.- 7 Singularities of the Stability Boundary and the Principle of the Fragility of Good Things.- 8 Caustics, Wave Fronts, and Their Metamorphoses.- 9 The Large-Scale Distribution of Matter in the Universe.- 10 Singularities in Optimization Problems: the Maximum function.- 11 Singularities of the Boundary of Attainability.- 12 Smooth Surfaces and Their Projections.- 13 The Problem of Bypassing an Obstacle.- 14 Symplectic and Contact Geometry.- 15 Complex Singularities.- 16 The Mysticism of Catastrophe Theory.- Appendix The Precursors of Catastrophe Theory.- Conclusion.- Problems.- References.
Synopsis
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., This well-known booklet, now in its third, expanded edition, provides an informal survey of applications of singularity theory in a wide range of areas. Although the first few chapters touch briefly (and critically) on theThom-Zeeman catastrophe theory, most of the book is concerned with more recent and less controversial aspects, covering such topics as: bifurcations and stability loss, wavefront propagation, the distribution of matter in the universe, optimization and control problems, visible contours,bypassing an obstacle, symplectic and contact geometry, complex singularities, and the surprising connections between singularities and widely disparate mathematical objects such as regular polyhedra and reflection groups. Readers familiar with the previous editions will find much that is new. Results have been brought up to date, and among the new or expanded topics discussed are delayed loss of stability, cascades of period doublings and triplings, shock waves, implicit differential equationsand folded singularities, interior scattering, and more. Three new sections give an overview of the history of singularity theory and its applications from Leonardo da Vinci to modern times, a discussion of perestroika in terms of the theory of metamorphoses, and a list of 93 problems touching on most of the subject matter in the book. The text is enhanced by fifteen new drawings (there are now 87 in all) and improvements to old ones. The already extensive literature list has been updated and expanded. As a result, the book has been enlarged by almost a third. Arnol'd's goal with this edition remains the same: to explain the essence of the results and applications to readers having a minimal mathematical background. All that he asks, is that the reader have an inquiring mind.
LC Classification Number
QA299.6-433
Item description from the seller
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- n***h (860)- Feedback left by buyer.Past 6 monthsVerified purchaseGreat eBay seller. Perfect transaction. Fast shipping. Expert packing job/materials. Very reasonable shipping charges. Excellent customer service and communications. Item description was/is right on. Very pleased all the way around. Five stars for sure. THANK YOU!!Strauss: Operas (#156607876078)
- 2***o (142)- Feedback left by buyer.Past 6 monthsVerified purchaseAs described in perfect condition no damage to whole lot handled with care very good price package with bubble wrap appearance fantastic very brand new quality fantastic fantastic definently recommend ships rite away no waiting AAA+++ definently coming back thank you seller
- m***m (115)- Feedback left by buyer.Past 6 monthsVerified purchaseShipping was fast. The game was very well packaged and wrapped with a hard cardboard to protect it during shipment. Game is as described. Manual, disc and insert are flawless. Not a single scratch on the disc. It looks brand new. Very happy with my purchase. Thank you!!!!
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Seller feedback (2,680)
- n***h (860)- Feedback left by buyer.Past 6 monthsVerified purchaseGreat eBay seller. Perfect transaction. Fast shipping. Expert packing job/materials. Very reasonable shipping charges. Excellent customer service and communications. Item description was/is right on. Very pleased all the way around. Five stars for sure. THANK YOU!!Strauss: Operas (#156607876078)
- 2***o (142)- Feedback left by buyer.Past 6 monthsVerified purchaseAs described in perfect condition no damage to whole lot handled with care very good price package with bubble wrap appearance fantastic very brand new quality fantastic fantastic definently recommend ships rite away no waiting AAA+++ definently coming back thank you seller
- m***m (115)- Feedback left by buyer.Past 6 monthsVerified purchaseShipping was fast. The game was very well packaged and wrapped with a hard cardboard to protect it during shipment. Game is as described. Manual, disc and insert are flawless. Not a single scratch on the disc. It looks brand new. Very happy with my purchase. Thank you!!!!