Singularities And Groups In Bifurcation Theory

Author : Martin Golubitsky,David G. Schaeffer
Publisher : Springer Science & Business Media
Page : 480 pages
File Size : 44,8 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9781461250340

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Singularities and Groups in Bifurcation Theory by Martin Golubitsky,David G. Schaeffer Pdf

This book has been written in a frankly partisian spirit-we believe that singularity theory offers an extremely useful approach to bifurcation prob lems and we hope to convert the reader to this view. In this preface we will discuss what we feel are the strengths of the singularity theory approach. This discussion then Ieads naturally into a discussion of the contents of the book and the prerequisites for reading it. Let us emphasize that our principal contribution in this area has been to apply pre-existing techniques from singularity theory, especially unfolding theory and classification theory, to bifurcation problems. Many ofthe ideas in this part of singularity theory were originally proposed by Rene Thom; the subject was then developed rigorously by John Matherand extended by V. I. Arnold. In applying this material to bifurcation problems, we were greatly encouraged by how weil the mathematical ideas of singularity theory meshed with the questions addressed by bifurcation theory. Concerning our title, Singularities and Groups in Bifurcation Theory, it should be mentioned that the present text is the first volume in a two-volume sequence. In this volume our emphasis is on singularity theory, with group theory playing a subordinate role. In Volume II the emphasis will be more balanced. Having made these remarks, Iet us set the context for the discussion of the strengths of the singularity theory approach to bifurcation. As we use the term, bifurcation theory is the study of equations with multiple solutions.

Author : Martin Golubitsky,David G. Schaeffer
Publisher : Springer
Page : 466 pages
File Size : 51,8 Mb
Release : 1984-12-05
Category : Mathematics
ISBN : 0387909990

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Singularities and Groups in Bifurcation Theory by Martin Golubitsky,David G. Schaeffer Pdf

This book has been written in a frankly partisian spirit-we believe that singularity theory offers an extremely useful approach to bifurcation prob lems and we hope to convert the reader to this view. In this preface we will discuss what we feel are the strengths of the singularity theory approach. This discussion then Ieads naturally into a discussion of the contents of the book and the prerequisites for reading it. Let us emphasize that our principal contribution in this area has been to apply pre-existing techniques from singularity theory, especially unfolding theory and classification theory, to bifurcation problems. Many ofthe ideas in this part of singularity theory were originally proposed by Rene Thom; the subject was then developed rigorously by John Matherand extended by V. I. Arnold. In applying this material to bifurcation problems, we were greatly encouraged by how weil the mathematical ideas of singularity theory meshed with the questions addressed by bifurcation theory. Concerning our title, Singularities and Groups in Bifurcation Theory, it should be mentioned that the present text is the first volume in a two-volume sequence. In this volume our emphasis is on singularity theory, with group theory playing a subordinate role. In Volume II the emphasis will be more balanced. Having made these remarks, Iet us set the context for the discussion of the strengths of the singularity theory approach to bifurcation. As we use the term, bifurcation theory is the study of equations with multiple solutions.

Author : Martin Golubitsky,Ian Stewart,David G. Schaeffer
Publisher : Springer Science & Business Media
Page : 551 pages
File Size : 45,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461245742

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Singularities and Groups in Bifurcation Theory by Martin Golubitsky,Ian Stewart,David G. Schaeffer Pdf

Bifurcation theory studies how the structure of solutions to equations changes as parameters are varied. The nature of these changes depends both on the number of parameters and on the symmetries of the equations. Volume I discusses how singularity-theoretic techniques aid the understanding of transitions in multiparameter systems. This volume focuses on bifurcation problems with symmetry and shows how group-theoretic techniques aid the understanding of transitions in symmetric systems. Four broad topics are covered: group theory and steady-state bifurcation, equicariant singularity theory, Hopf bifurcation with symmetry, and mode interactions. The opening chapter provides an introduction to these subjects and motivates the study of systems with symmetry. Detailed case studies illustrate how group-theoretic methods can be used to analyze specific problems arising in applications.

Author : Martin Golubitsky,Ian Stewart,David G Schaeffer
Publisher : Unknown
Page : 556 pages
File Size : 40,9 Mb
Release : 1988-06-01
Category : Electronic
ISBN : 1461245753

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Singularities and Groups in Bifurcation Theory by Martin Golubitsky,Ian Stewart,David G Schaeffer Pdf

Author : Martin Golubitsky,David G. Schaeffer
Publisher : Springer
Page : 0 pages
File Size : 49,7 Mb
Release : 1984-12-05
Category : Mathematics
ISBN : 0387909990

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Singularities and Groups in Bifurcation Theory by Martin Golubitsky,David G. Schaeffer Pdf

This book has been written in a frankly partisian spirit-we believe that singularity theory offers an extremely useful approach to bifurcation prob lems and we hope to convert the reader to this view. In this preface we will discuss what we feel are the strengths of the singularity theory approach. This discussion then Ieads naturally into a discussion of the contents of the book and the prerequisites for reading it. Let us emphasize that our principal contribution in this area has been to apply pre-existing techniques from singularity theory, especially unfolding theory and classification theory, to bifurcation problems. Many ofthe ideas in this part of singularity theory were originally proposed by Rene Thom; the subject was then developed rigorously by John Matherand extended by V. I. Arnold. In applying this material to bifurcation problems, we were greatly encouraged by how weil the mathematical ideas of singularity theory meshed with the questions addressed by bifurcation theory. Concerning our title, Singularities and Groups in Bifurcation Theory, it should be mentioned that the present text is the first volume in a two-volume sequence. In this volume our emphasis is on singularity theory, with group theory playing a subordinate role. In Volume II the emphasis will be more balanced. Having made these remarks, Iet us set the context for the discussion of the strengths of the singularity theory approach to bifurcation. As we use the term, bifurcation theory is the study of equations with multiple solutions.

Author : Mark Roberts,Ian Stewart
Publisher : Springer
Page : 344 pages
File Size : 46,6 Mb
Release : 1991-07-10
Category : Mathematics
ISBN : 3540537368

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Singularity Theory and its Applications by Mark Roberts,Ian Stewart Pdf

A workshop on Singularities, Bifuraction and Dynamics was held at Warwick in July 1989, as part of a year-long symposium on Singularity Theory and its applications. The proceedings fall into two halves: Volume I mainly on connections with algebraic geometry and volume II on connections with dynamical systems theory, bifurcation theory and applications in the sciences. The papers are original research, stimulated by the symposium and workshop: All have been refereed and none will appear elsewhere. The main topic of volume II is new methods for the study of bifurcations in nonlinear dynamical systems, and applications of these.

Author : James Montaldi
Publisher : Cambridge University Press
Page : 449 pages
File Size : 50,6 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 : Kiyohiro Ikeda,Kazuo Murota
Publisher : Springer Science & Business Media
Page : 313 pages
File Size : 50,5 Mb
Release : 2013-11-08
Category : Technology & Engineering
ISBN : 9784431542582

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Bifurcation Theory for Hexagonal Agglomeration in Economic Geography by Kiyohiro Ikeda,Kazuo Murota Pdf

This book contributes to an understanding of how bifurcation theory adapts to the analysis of economic geography. It is easily accessible not only to mathematicians and economists, but also to upper-level undergraduate and graduate students who are interested in nonlinear mathematics. The self-organization of hexagonal agglomeration patterns of industrial regions was first predicted by the central place theory in economic geography based on investigations of southern Germany. The emergence of hexagonal agglomeration in economic geography models was envisaged by Krugman. In this book, after a brief introduction of central place theory and new economic geography, the missing link between them is discovered by elucidating the mechanism of the evolution of bifurcating hexagonal patterns. Pattern formation by such bifurcation is a well-studied topic in nonlinear mathematics, and group-theoretic bifurcation analysis is a well-developed theoretical tool. A finite hexagonal lattice is used to express uniformly distributed places, and the symmetry of this lattice is expressed by a finite group. Several mathematical methodologies indispensable for tackling the present problem are gathered in a self-contained manner. The existence of hexagonal distributions is verified by group-theoretic bifurcation analysis, first by applying the so-called equivariant branching lemma and next by solving the bifurcation equation. This book offers a complete guide for the application of group-theoretic bifurcation analysis to economic agglomeration on the hexagonal lattice.

Author : Martin Golubitsky
Publisher : American Mathematical Soc.
Page : 387 pages
File Size : 41,9 Mb
Release : 1986
Category : Mathematics
ISBN : 9780821850602

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Multiparameter Bifurcation Theory by Martin Golubitsky Pdf

The 1985 AMS Summer Research Conference brought together mathematicians interested in multiparameter bifurcation with scientists working on fluid instabilities and chemical reactor dynamics. This work demonstrates the mutually beneficial interactions between the mathematical analysis, based on genericity, and experimental studies in these fields.

Author : Denis Ch‚niot
Publisher : World Scientific
Page : 1083 pages
File Size : 45,5 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812704108

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Singularity Theory by Denis Ch‚niot Pdf

The Singularity School and Conference took place in Luminy, Marseille, from January 24th to February 25th 2005. More than 180 mathematicians from over 30 countries converged to discuss recent developments in singularity theory.The volume contains the elementary and advanced courses conducted by singularities specialists during the conference, general lectures on singularity theory, and lectures on applications of the theory to various domains. The subjects range from geometry and topology of singularities, through real and complex singularities, to applications of singularities.

Author : Thomas J. Bridges,Jacques E. Furter
Publisher : Springer
Page : 227 pages
File Size : 41,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540480402

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Singularity Theory and Equivariant Symplectic Maps by Thomas J. Bridges,Jacques E. Furter Pdf

The monograph is a study of the local bifurcations of multiparameter symplectic maps of arbitrary dimension in the neighborhood of a fixed point.The problem is reduced to a study of critical points of an equivariant gradient bifurcation problem, using the correspondence between orbits ofa symplectic map and critical points of an action functional. New results onsingularity theory for equivariant gradient bifurcation problems are obtained and then used to classify singularities of bifurcating period-q points. Of particular interest is that a general framework for analyzing group-theoretic aspects and singularities of symplectic maps (particularly period-q points) is presented. Topics include: bifurcations when the symplectic map has spatial symmetry and a theory for the collision of multipliers near rational points with and without spatial symmetry. The monograph also includes 11 self-contained appendices each with a basic result on symplectic maps. The monograph will appeal to researchers and graduate students in the areas of symplectic maps, Hamiltonian systems, singularity theory and equivariant bifurcation theory.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 43,9 Mb
Release : 2024-06-02
Category : Electronic
ISBN : 9789814476393

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Singularity Theory by Anonim Pdf

Author : Hansjörg Kielhöfer
Publisher : Springer Science & Business Media
Page : 355 pages
File Size : 54,8 Mb
Release : 2006-04-10
Category : Mathematics
ISBN : 9780387216331

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Bifurcation Theory by Hansjörg Kielhöfer Pdf

In the past three decades, bifurcation theory has matured into a well-established and vibrant branch of mathematics. This book gives a unified presentation in an abstract setting of the main theorems in bifurcation theory, as well as more recent and lesser known results. It covers both the local and global theory of one-parameter bifurcations for operators acting in infinite-dimensional Banach spaces, and shows how to apply the theory to problems involving partial differential equations. In addition to existence, qualitative properties such as stability and nodal structure of bifurcating solutions are treated in depth. This volume will serve as an important reference for mathematicians, physicists, and theoretically-inclined engineers working in bifurcation theory and its applications to partial differential equations.

Author : Tian Ma,Shouhong Wang
Publisher : World Scientific
Page : 391 pages
File Size : 48,6 Mb
Release : 2005
Category : Mathematics
ISBN : 9789812701152

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Bifurcation Theory and Applications by Tian Ma,Shouhong Wang Pdf

This book covers comprehensive bifurcation theory and its applications to dynamical systems and partial differential equations (PDEs) from science and engineering, including in particular PDEs from physics, chemistry, biology, and hydrodynamics. The book first introduces bifurcation theories recently developed by the authors, on steady state bifurcation for a class of nonlinear problems with even order nondegenerate nonlinearities, regardless of the multiplicity of the eigenvalues, and on attractor bifurcations for nonlinear evolution equations, a new notion of bifurcation. With this new notion of bifurcation, many longstanding bifurcation problems in science and engineering are becoming accessible, and are treated in the second part of the book. In particular, applications are covered for a variety of PDEs from science and engineering, including the KuramotoOCoSivashinsky equation, the CahnOCoHillard equation, the GinzburgOCoLandau equation, reaction-diffusion equations in biology and chemistry, the Benard convection problem, and the Taylor problem. The applications provide, on the one hand, general recipes for other applications of the theory addressed in this book, and on the other, full classifications of the bifurcated attractor and the global attractor as the control parameters cross certain critical values, dictated usually by the eigenvalues of the linearized problems. It is expected that the book will greatly advance the study of nonlinear dynamics for many problems in science and engineering."

Author : Yuri A. Kuznetsov
Publisher : Springer Science & Business Media
Page : 529 pages
File Size : 45,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475724219

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Elements of Applied Bifurcation Theory by Yuri A. Kuznetsov Pdf

A solid basis for anyone studying the dynamical systems theory, providing the necessary understanding of the approaches, methods, results and terminology used in the modern applied-mathematics literature. Covering the basic topics in the field, the text can be used in a course on nonlinear dynamical systems or system theory. Special attention is given to efficient numerical implementations of the developed techniques, illustrated by several examples from recent research papers. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used, making this book suitable for advanced undergraduate or graduate students in applied mathematics, as well as for researchers in other disciplines who use dynamical systems as model tools in their studies.