Singularities And Groups In Bifurcation Theory
DOWNLOAD
Download Singularities And Groups In Bifurcation Theory PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Singularities And Groups In Bifurcation Theory book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Singularities And Groups In Bifurcation Theory
DOWNLOAD
Author : Martin Golubitsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Singularities And Groups In Bifurcation Theory written by Martin Golubitsky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Mathematics categories.
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.
Singularities And Groups In Bifurcation Theory
DOWNLOAD
Author : Martin Golubitsky
language : en
Publisher: Springer
Release Date : 1984-12-05
Singularities And Groups In Bifurcation Theory written by Martin Golubitsky and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-12-05 with Mathematics categories.
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.
Singularities And Groups In Bifurcation Theory
DOWNLOAD
Author : Martin Golubitsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Singularities And Groups In Bifurcation Theory written by Martin Golubitsky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Singularities And Groups In Bifurcation Theory
DOWNLOAD
Author : Martin Golubitsky
language : en
Publisher: Springer
Release Date : 2000-09-05
Singularities And Groups In Bifurcation Theory written by Martin Golubitsky and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-09-05 with Mathematics categories.
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.
Singularities Bifurcations And Catastrophes
DOWNLOAD
Author : James Montaldi
language : en
Publisher: Cambridge University Press
Release Date : 2021-06-24
Singularities Bifurcations And Catastrophes written by James Montaldi and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-24 with Mathematics categories.
This textbook gives a contemporary account of singularity theory and its principal application, bifurcation theory.
Elements Of Applied Bifurcation Theory
DOWNLOAD
Author : Yuri A. Kuznetsov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Elements Of Applied Bifurcation Theory written by Yuri A. Kuznetsov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
During the last few years several good textbooks on nonlinear dynamics have ap peared for graduate students in applied mathematics. It seems, however, that the majority of such books are still too theoretically oriented and leave many practi cal issues unclear for people intending to apply the theory to particular research problems. This book is designed for advanced undergraduate or graduate students in mathematics who will participate in applied research. It is also addressed to professional researchers in physics, biology, engineering, and economics who use dynamical systems as modeling tools in their studies. Therefore, only a moderate mathematical background in geometry, linear algebra, analysis, and differential equations is required. A brief summary of general mathematical terms and results that are assumed to be known in the main text appears at the end of the book. Whenever possible, only elementary mathematical tools are used. For example, we do not try to present normal form theory in full generality, instead developing only the portion of the technique sufficient for our purposes. The book aims to provide the student (or researcher) with both a solid basis in dynamical systems theory and the necessary understanding of the approaches, methods, results, and terminology used in the modem applied mathematics litera ture. A key theme is that of topological equivalence and codimension, or "what one may expect to occur in the dynamics with a given number of parameters allowed to vary.
Singularity Theory I
DOWNLOAD
Author : V.I. Arnold
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Singularity Theory I written by V.I. Arnold and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
From the reviews: "... My general impression is of a particularly nice book, with a well-balanced bibliography, recommended!" Mededelingen van Het Wiskundig Genootschap, 1995 "... The authors offer here an up to date guide to the topic and its main applications, including a number of new results. It is very convenient for the reader, a carefully prepared and extensive bibliography ... makes it easy to find the necessary details when needed. The books (EMS 6 and EMS 39) describe a lot of interesting topics. ... Both volumes are a very valuable addition to the library of any mathematician or physicist interested in modern mathematical analysis." European Mathematical Society Newsletter, 1994
Lectures On Bifurcations Dynamics And Symmetry
DOWNLOAD
Author : Michael J. Field
language : en
Publisher: CRC Press
Release Date : 2020-02-17
Lectures On Bifurcations Dynamics And Symmetry written by Michael J. Field and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-17 with Mathematics categories.
This book is an expanded version of a Master Class on the symmetric bifurcation theory of differential equations given by the author at the University of Twente in 1995. The notes cover a wide range of recent results in the subject, and focus on the dynamics that can appear in the generic bifurcation theory of symmetric differential equations. This text covers a wide range of current results in the subject of bifurcations, dynamics and symmetry. The style and format of the original lectures has largely been maintained and the notes include over 70 exercises.
Practical Bifurcation And Stability Analysis
DOWNLOAD
Author : Rüdiger Seydel
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-14
Practical Bifurcation And Stability Analysis written by Rüdiger Seydel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-14 with Mathematics categories.
Probably the first book to describe computational methods for numerically computing steady state and Hopf bifurcations. Requiring only a basic knowledge of calculus, and using detailed examples, problems, and figures, this is an ideal textbook for graduate students.
Methods In Equivariant Bifurcations And Dynamical Systems
DOWNLOAD
Author : Pascal Chossat
language : en
Publisher: World Scientific Publishing Company
Release Date : 2000-02-28
Methods In Equivariant Bifurcations And Dynamical Systems written by Pascal Chossat and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-02-28 with Science categories.
This invaluable book presents a comprehensive introduction to bifurcation theory in the presence of symmetry, an applied mathematical topic which has developed considerably over the past twenty years and has been very successful in analysing and predicting pattern formation and other critical phenomena in most areas of science where nonlinear models are involved, like fluid flow instabilities, chemical waves, elasticity and population dynamics.The book has two aims. One is to expound the mathematical methods of equivariant bifurcation theory. Beyond the classical bifurcation tools, such as center manifold and normal form reductions, the presence of symmetry requires the introduction of the algebraic and geometric formalism of Lie group theory and transformation group methods. For the first time, all these methods in equivariant bifurcations are presented in a coherent and self-consistent way in a book.The other aim is to present the most recent ideas and results in this theory, in relation to applications. This includes bifurcations of relative equilibria and relative periodic orbits for compact and noncompact group actions, heteroclinic cycles and forced symmetry-breaking perturbations. Although not all recent contributions could be included and a choice had to be made, a rather complete description of these new developments is provided. At the end of every chapter, exercises are offered to the reader.