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Singularities and Groups in Bifurcation Theory: Volume I (Applied Mathematical Sciences)

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ISBN: 0387909990

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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 applied,differential equations,geometry,geometry and topology,group theory,mathematical analysis,mathematics,pure mathematics,science and math,science and math Mathematics, Springer

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ISBN: 9780387909998

[ED: Hardcover], [PU: Springer, Berlin], 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.xviii, 466 S. 18 Tabellen. 234 mmVersandfertig in 3-5 Tagen, [SC: 0.00]

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ISBN: 9780387909998

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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: Volume 1 Golubitsky, Martin / Schaeffer, David G., Springer

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ISBN: 9780387909998

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Singularities and Groups in Bifurcation Theory: Volume I Singularities-and-Groups-in-Bifurcation-Theory~~Martin-Golubitsky Science/Tech>Mathematics>Mathematics Hardcover, Springer New York

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Mathematics; Analysis; Geometry; Applications of Mathematics Area, Bifurcations, Group theory, Groups, Volume Books Book, Springer Science+Business Media

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** Details of the book - Singularities and Groups in Bifurcation Theory**

EAN (ISBN-13): 9780387909998

ISBN (ISBN-10): 0387909990

Hardcover

Publishing year: 2007

Publisher: Springer-Verlag GmbH

488 Pages

Weight: 0,888 kg

Language: eng/Englisch

Book in our database since 15.10.2007 22:04:04

Book found last time on 08.05.2017 10:32:09

ISBN/EAN: 0387909990

ISBN - alternate spelling:

0-387-90999-0, 978-0-387-90999-8

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