Bifurcations And Catastrophes

Author : Michel Demazure
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 49,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783642571343

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Bifurcations and Catastrophes by Michel Demazure Pdf

Based on a lecture course, this text gives a rigorous introduction to nonlinear analysis, dynamical systems and bifurcation theory including catastrophe theory. Wherever appropriate it emphasizes a geometrical or coordinate-free approach allowing a clear focus on the essential mathematical structures. It brings out features common to different branches of the subject while giving ample references for more advanced or technical developments.

Author : James Montaldi
Publisher : Cambridge University Press
Page : 449 pages
File Size : 54,9 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 : Michel Demazure,D Chillingworth
Publisher : Unknown
Page : 312 pages
File Size : 51,5 Mb
Release : 1999-12-15
Category : Electronic
ISBN : 3642571352

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Bifurcations and Catastrophes by Michel Demazure,D Chillingworth Pdf

Based on a lecture course, this text gives a rigorous introduction to nonlinear analysis, dynamical systems and bifurcation theory including catastrophe theory. Wherever appropriate it emphasizes a geometrical or coordinate-free approach allowing a clear focus on the essential mathematical structures. It brings out features common to different branches of the subject while giving ample references for more advanced or technical developments.

Author : V.I. Arnold,V.S. Afrajmovich,Yu.S. Il'yashenko,L.P. Shil'nikov
Publisher : Springer
Page : 0 pages
File Size : 53,7 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 : V.I. Arnold,V.S. Afrajmovich,Yu.S. Il'yashenko,L.P. Shil'nikov
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 40,8 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783642578847

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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 : V. I. Arnol'd
Publisher : Springer Science & Business Media
Page : 91 pages
File Size : 41,9 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 : V.I. Arnold,V.S. Afrajmovich,Yu.S. Il'yashenko,L.P. Shil'nikov
Publisher : Springer
Page : 274 pages
File Size : 40,7 Mb
Release : 2011-11-14
Category : Mathematics
ISBN : 3642578853

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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 : Vladimir I. Arnol'd
Publisher : Springer Science & Business Media
Page : 120 pages
File Size : 55,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642969379

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Catastrophe Theory by Vladimir I. Arnol'd Pdf

Author : Vladimir I. Arnol'd
Publisher : Springer Science & Business Media
Page : 174 pages
File Size : 43,7 Mb
Release : 2003-10-29
Category : Mathematics
ISBN : 3540548114

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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 : Yuri Kuznetsov
Publisher : Springer Science & Business Media
Page : 648 pages
File Size : 53,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475739787

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Elements of Applied Bifurcation Theory by Yuri Kuznetsov Pdf

Providing readers with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems, the focus here is on efficient numerical implementations of the developed techniques. The book is designed for advanced undergraduates or graduates in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the first while updating the context to incorporate recent theoretical developments, in particular new and improved numerical methods for bifurcation analysis.

Author : Koncay Huseyin
Publisher : Oxford University Press, USA
Page : 312 pages
File Size : 40,9 Mb
Release : 1986
Category : Philosophy
ISBN : STANFORD:36105030425735

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Multiple Parameter Stability Theory and Its Applications by Koncay Huseyin Pdf

Written from an original, engineering point of view, this volume presents a general nonlinear theory concerning the stability, instability, bifurcation, and oscillatory behavior of autonomous systems. Huseyin stresses analytical procedures which lead to construction of asymptotic solutions. He analyzes various bifurcation phenomena and the associated imperfection-sensitivities via the multiple-parameter perturbation technique, a method which generates distinct forms of equilibrium surfaces linked to "elementary catastrophes." In addition, he introduces an intrinsic harmonic balancing technique to analyze the dynamic bifurcations, resulting in a unified treatment of both static and dynamic bifurcation phenomena within an autonomous framework. Throughout the work, the presentation is conceptually simple and practical.

Author : V. I. Arnol'd
Publisher : Springer
Page : 79 pages
File Size : 48,9 Mb
Release : 1986-04-01
Category : Mathematics
ISBN : 354012859X

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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 : Tönu Puu
Publisher : Springer Science & Business Media
Page : 556 pages
File Size : 42,5 Mb
Release : 2013-03-19
Category : Mathematics
ISBN : 9783540246992

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Attractors, Bifurcations, & Chaos by Tönu Puu Pdf

Attractors, Bifurcations, & Chaos - now in its second edition - begins with an introduction to mathematical methods in modern nonlinear dynamics and deals with differential equations. Phenomena such as bifurcations and deterministic chaos are given considerable emphasis, both in the methodological part, and in the second part, containing various applications in economics and in regional science. Coexistence of attractors and the multiplicity of development paths in nonlinear systems are central topics. The applications focus on issues such as business cycles, oligopoly, interregional trade dynamics, and economic development theory.

Author : V.I. Arnold,V.S. Afrajmovich,Yu.S. Il'yashenko,L.P. Shil'nikov
Publisher : Springer
Page : 306 pages
File Size : 54,9 Mb
Release : 1994-06-06
Category : Mathematics
ISBN : 3540181733

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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 : John Casti
Publisher : John Wiley & Sons
Page : 414 pages
File Size : 49,8 Mb
Release : 1997-03-27
Category : Mathematics
ISBN : 0471184357

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Reality Rules, The Fundamentals by John Casti Pdf

Die beiden ursprünglich 1992 veröffentlichten Bände liegen nun in zusammengefaßter Paperback-Form vor. Reality Rules beleuchten die Syntax und die Semantik der Sprache, in der mathematische Modellierungsregeln niedergelegt werden. Eine Vielzahl von Beispielen zeigt praktische Anwendungen auf; auch ein Lösungsband zur Unterstützung des Selbststudiums ist erhältlich.