Singularity Theory And An Introduction To Catastrophe Theory

Author : Y.-C. Lu
Publisher : Springer
Page : 218 pages
File Size : 42,8 Mb
Release : 1976
Category : Gardening
ISBN : MINN:31951000552204M

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Singularity Theory and an Introduction to Catastrophe Theory by Y.-C. Lu Pdf

In April, 1975, I organised a conference at the Battelle Research Center, Seattle, Washington on the theme "Structural stability, catastrophe theory and their applications in the sciences". To this conference were invited a number of mathematicians concerned with the mathematical theories of structural stability and catastrophe theory, and other mathematicians whose principal interest lay in applications to various sciences - physical, biological, medical and social. Rene Thorn and Christopher Zeeman figured in the list of distinguished participants. The conference aroused considerable interest, and many mathematicians who were not specialists in the fields covered by the conference expressed their desire to attend the conference sessions; in addition, scientists from the Battelle laboratories came to Seattle to learn of developments in these areas and to consider possible applications to their own work. In view of the attendance of these mathematicians and scientists, and in order to enable the expositions of the experts to be intelligible to this wider audience, I invited Professor YungƯ Chen Lu, of Ohio State University, to come to Battelle Seattle in advance of the actual conference to deliver a series of informal lecture-seminars, explaining the background of the mathematical theory and indicating some of the actual and possible applications. In the event, Yung-Chen Lu delivered his lectures in the week preceding and the week following the actual conference, so that the first half of his course was preparatory and the second half explanatory and evaluative. These lecture notes constitute an expanded version of the course

Author : Yung-Chen Lu
Publisher : Unknown
Page : 199 pages
File Size : 54,9 Mb
Release : 1976
Category : Catastrophes (Mathematics)
ISBN : 354090221X

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Singularity Theory and an Introduction to Catastrophe Theory by Yung-Chen Lu Pdf

Author : Vladimir I. Arnol'd
Publisher : Springer Science & Business Media
Page : 161 pages
File Size : 55,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642581243

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Catastrophe Theory by Vladimir I. Arnol'd Pdf

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.

Author : V. I. Arnol'd
Publisher : Springer Science & Business Media
Page : 91 pages
File Size : 43,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642967993

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Catastrophe Theory by V. I. Arnol'd Pdf

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 .

Author : Y.-C. Lu
Publisher : Springer Science & Business Media
Page : 212 pages
File Size : 50,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461299097

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Singularity Theory and an Introduction to Catastrophe Theory by Y.-C. Lu Pdf

In April, 1975, I organised a conference at the Battelle Research Center, Seattle, Washington on the theme "Structural stability, catastrophe theory and their applications in the sciences". To this conference were invited a number of mathematicians concerned with the mathematical theories of structural stability and catastrophe theory, and other mathematicians whose principal interest lay in applications to various sciences - physical, biological, medical and social. Rene Thorn and Christopher Zeeman figured in the list of distinguished participants. The conference aroused considerable interest, and many mathematicians who were not specialists in the fields covered by the conference expressed their desire to attend the conference sessions; in addition, scientists from the Battelle laboratories came to Seattle to learn of developments in these areas and to consider possible applications to their own work. In view of the attendance of these mathematicians and scientists, and in order to enable the expositions of the experts to be intelligible to this wider audience, I invited Professor Yung Chen Lu, of Ohio State University, to come to Battelle Seattle in advance of the actual conference to deliver a series of informal lecture-seminars, explaining the background of the mathematical theory and indicating some of the actual and possible applications. In the event, Yung-Chen Lu delivered his lectures in the week preceding and the week following the actual conference, so that the first half of his course was preparatory and the second half explanatory and evaluative. These lecture notes constitute an expanded version of the course.

Author : Vladimir Igorevich Arnolʹd
Publisher : Springer
Page : 142 pages
File Size : 41,6 Mb
Release : 1986
Category : Mathematics
ISBN : UVA:X001468629

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Catastrophe Theory by Vladimir Igorevich Arnolʹd Pdf

From the reviews: "This is a short, critical and nonmathematical review of catastrophe theory which will provide a useful introduction to the subject". Physics Bulletin.

Author : James Montaldi
Publisher : Cambridge University Press
Page : 449 pages
File Size : 55,5 Mb
Release : 2021-06-24
Category : Mathematics
ISBN : 9781107151642

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Singularities, Bifurcations and Catastrophes by James Montaldi Pdf

This textbook gives a contemporary account of singularity theory and its principal application, bifurcation theory.

Author : Peter Timothy Saunders
Publisher : Cambridge University Press
Page : 162 pages
File Size : 41,8 Mb
Release : 1980-06-30
Category : Mathematics
ISBN : 0521297826

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An Introduction to Catastrophe Theory by Peter Timothy Saunders Pdf

An introduction to catastrophe theory, a mathematical theory which deals with those changes which occur abruptly rather than smoothly. Includes many applications to illustrate the different ways in which catastrophe can be used in life, physical and social sciences.

Author : Domencio Castrigiano,Sandra Hayes
Publisher : CRC Press
Page : 281 pages
File Size : 43,6 Mb
Release : 2019-06-03
Category : Mathematics
ISBN : 9780429970351

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Catastrophe Theory by Domencio Castrigiano,Sandra Hayes Pdf

Catastrophe Theory was introduced in the 1960s by the renowned Fields Medal mathematician René Thom as a part of the general theory of local singularities. Since then it has found applications across many areas, including biology, economics, and chemical kinetics. By investigating the phenomena of bifurcation and chaos, Catastrophe Theory proved to

Author : Arlie O. Petters,Harold Levine,Joachim Wambsganss
Publisher : Springer Science & Business Media
Page : 616 pages
File Size : 42,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461201458

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Singularity Theory and Gravitational Lensing by Arlie O. Petters,Harold Levine,Joachim Wambsganss Pdf

This monograph is the first to develop a mathematical theory of gravitational lensing. The theory applies to any finite number of deflector planes and highlights the distinctions between single and multiple plane lensing. Introductory material in Parts I and II present historical highlights and the astrophysical aspects of the subject. Part III employs the ideas and results of singularity theory to put gravitational lensing on a rigorous mathematical foundation.

Author : John F. Pierce
Publisher : Springer
Page : 182 pages
File Size : 47,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540461906

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Singularity Theory, Rod Theory, and Symmetry Breaking Loads by John F. Pierce Pdf

Author : Robert A. Meyers
Publisher : Springer Science & Business Media
Page : 1885 pages
File Size : 42,6 Mb
Release : 2011-10-05
Category : Mathematics
ISBN : 9781461418054

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Mathematics of Complexity and Dynamical Systems by Robert A. Meyers Pdf

Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

Author : V.I. Arnold,V.S. Afrajmovich,Yu.S. Il'yashenko,L.P. Shil'nikov
Publisher : Springer
Page : 0 pages
File Size : 51,7 Mb
Release : 1999-05-20
Category : Mathematics
ISBN : 3540653791

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Dynamical Systems V by V.I. Arnold,V.S. Afrajmovich,Yu.S. Il'yashenko,L.P. Shil'nikov Pdf

Bifurcation theory and catastrophe theory are two well-known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics", such as the characterization of personalities and the difference between a "genius" and a "maniac". Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, previously published as Volume 5 of the Encyclopaedia, have given a masterly exposition of these two theories, with penetrating insight.

Author : Adam Coffman
Publisher : American Mathematical Soc.
Page : 105 pages
File Size : 53,7 Mb
Release : 2010
Category : CR submanifolds
ISBN : 9780821846575

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Unfolding CR Singularities by Adam Coffman Pdf

"Volume 205, number 962 (first of 5 numbers)."

Author : D.W. Stroock
Publisher : Springer Science & Business Media
Page : 204 pages
File Size : 44,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461385141

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An Introduction to the Theory of Large Deviations by D.W. Stroock Pdf

These notes are based on a course which I gave during the academic year 1983-84 at the University of Colorado. My intention was to provide both my audience as well as myself with an introduction to the theory of 1arie deviations • The organization of sections 1) through 3) owes something to chance and a great deal to the excellent set of notes written by R. Azencott for the course which he gave in 1978 at Saint-Flour (cf. Springer Lecture Notes in Mathematics 774). To be more precise: it is chance that I was around N. Y. U. at the time'when M. Schilder wrote his thesis. and so it may be considered chance that I chose to use his result as a jumping off point; with only minor variations. everything else in these sections is taken from Azencott. In particular. section 3) is little more than a rewrite of his exoposition of the Cramer theory via the ideas of Bahadur and Zabel. Furthermore. the brief treatment which I have given to the Ventsel-Freidlin theory in section 4) is again based on Azencott's ideas. All in all. the biggest difference between his and my exposition of these topics is the language in which we have written. However. another major difference must be mentioned: his bibliography is extensive and constitutes a fine introduction to the available literature. mine shares neither of these attributes. Starting with section 5).