- Taschenbuch: 150 Seiten
- Verlag: Springer Berlin Heidelberg; Auflage: 3rd, rev. and exp. ed. 1992. 2nd printing (22. Juli 1992)
- Sprache: Englisch
- ISBN-10: 3540548114
- ISBN-13: 978-3540548119
- Größe und/oder Gewicht: 20,4 x 16,5 x 1 cm
- Durchschnittliche Kundenbewertung: 5.0 von 5 Sternen Alle Rezensionen anzeigen (2 Kundenrezensionen)
- Amazon Bestseller-Rang: Nr. 346.306 in Englische Bücher (Siehe Top 100 in Englische Bücher)
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Produktbeschreibungen
Pressestimmen
"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
Kurzbeschreibung
In der dritten Auflage dieses bemerkenswerten Buches hat Arnold den Text gründlich überarbeitet und Aufgaben sowie einen Anhang zur Geschichte der Katastrophentheorie hinzugefügt. Arnold bringt seinen Lesern die Ideen der Katastrophentheorie nahe. Dabei setzt er lediglich voraus, daß der Leser bereit ist, sich auf ein mathematisches Abenteuer einzulassen
-- Dieser Text bezieht sich auf eine vergriffene oder nicht verfügbare Ausgabe dieses Titels.
In diesem Buch
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1 von 1 Kunden fanden die folgende Rezension hilfreich
Format:Taschenbuch
Catastrophe theory was the first mathematical "advance" to receive extensive coverage in the popular press since quantum mechanics. The interest and adulation afforded to chaos theory and nonlinear dynamical systems research barely immitated the enthusiasm and later scorn generated by Thom and his followers. In retrospect it is hard to see what all the excitement was about. Perhaps that's exactly why this book deserves serious attention.
While the doctoral trained mathematician may find more faults here than the rest of us, this book provides sufficient complexity for the professional, and at times is "gentle" enough for the nonmathematician. It will probably find its most useful audience among people with "semi-mathematical" trainings, scientists in life and behavioral or social sciences. For these people, who may just want to find out why Thom's initial theorems generated so much excitement and controversey, this book will be a readable delight.
This book should be mandatory reading for anyone claiming an interest in chaos theory but who does not understand how some of the overzealousness of a new paradigm can have devestating consequences. Needless to say, those unfamiliar with contemporary mathematical advances and behavioral/life/physical applications in European literarature will find this book invaluable.
0 von 1 Kunden fanden die folgende Rezension hilfreich
Format:Taschenbuch
Catastrophe theory was the first mathematical "advance" to receive extensive coverage in the popular press since quantum mechanics. The interest and adulation afforded to chaos theory and nonlinear dynamical systems research barely immitated the enthusiasm and later scorn generated by Thom and his followers. In retrospect it is hard to see what all the excitement was about. Perhaps that's exactly why this book deserves serious attention.
While the doctoral trained mathematician may find more faults here than the rest of us, this book provides sufficient complexity for the professional, and at times is "gentle" enough for the nonmathematician. It will probably find its most useful audience among people with "semi-mathematical" trainings, scientists in life and behavioral or social sciences. For these people, who may just want to find out why Thom's initial theorems generated so much excitement and controversey, this book will be a readable delight.
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5 von 5 Kunden fanden die folgende Rezension hilfreich
Singularity theory
30. Januar 2006
Format:Taschenbuch
Catastrophe theory is introduced as a sort of merger of Whitney's theory of singularities of mappings and Poincaré's qualitative theory of dynamical systems. First Whitney. A surface is projected onto a plane. Somewhere the surface is folded, so that the inverse of the projection is multi-valued. Now, the plane may represent the possible values of the control parameters of a dynamic system, and the surface the possible states of the system. Moving continuously in the plane across the boundary between a single-valued and a multi-valued region may cause a jump on the surface to one of the other sheets--i.e. a small external change causes the system's state to change drastically: a "catastrophe". Poincaré's bifurcation theory of dynamical systems may now be perceived similarly on a metalevel where the systems themselves are points in a space--again an infinitesimal move in the system space may cause drastic changes of the system's equilibria. This type of geometric thinking may then be used in applications--but only sober ones, mind you: elasticity, optics, etc. Back in the old days Thom quite successfully pushed his catastrophe theory on gullible non-mathematicians. Arnol'd states his own view on those matters clearly and repeatedly throughout the book. From the preface: "Neither in 1965 nor later was I ever able to understand a word of Thom's own talks on catastrophes. He once described them to me as 'bla, bla, bla'". Arnol'd instead prefers the mathematical meat and potatoes of catastrophe theory: the theory of singularities. If only one were as enthusiastic as Arnol'd about singularity classification theorems then this would be very interesting indeed.
12 von 15 Kunden fanden die folgende Rezension hilfreich
Outstanding introduction for life and behavioral scientists.
11. Dezember 1998
Format:Taschenbuch
Catastrophe theory was the first mathematical "advance" to receive extensive coverage in the popular press since quantum mechanics. The interest and adulation afforded to chaos theory and nonlinear dynamical systems research barely immitated the enthusiasm and later scorn generated by Thom and his followers. In retrospect it is hard to see what all the excitement was about. Perhaps that's exactly why this book deserves serious attention.
While the doctoral trained mathematician may find more faults here than the rest of us, this book provides sufficient complexity for the professional, and at times is "gentle" enough for the nonmathematician. It will probably find its most useful audience among people with "semi-mathematical" trainings, scientists in life and behavioral or social sciences. For these people, who may just want to find out why Thom's initial theorems generated so much excitement and controversey, this book will be a readable delight.
2 von 2 Kunden fanden die folgende Rezension hilfreich
Outstanding introduction for life and behavioral scientists.
11. Dezember 1998
Format:Taschenbuch
Catastrophe theory was the first mathematical "advance" to receive extensive coverage in the popular press since quantum mechanics. The interest and adulation afforded to chaos theory and nonlinear dynamical systems research barely immitated the enthusiasm and later scorn generated by Thom and his followers. In retrospect it is hard to see what all the excitement was about. Perhaps that's exactly why this book deserves serious attention.
While the doctoral trained mathematician may find more faults here than the rest of us, this book provides sufficient complexity for the professional, and at times is "gentle" enough for the nonmathematician. It will probably find its most useful audience among people with "semi-mathematical" trainings, scientists in life and behavioral or social sciences. For these people, who may just want to find out why Thom's initial theorems generated so much excitement and controversey, this book will be a readable delight.
This book should be mandatory reading for anyone claiming an interest in chaos theory but who does not understand how some of the overzealousness of a new paradigm can have devestating consequences. Needless to say, those unfamiliar with contemporary mathematical advances and behavioral/life/physical applications in European literarature will find this book invaluable.
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