Singularities and Groups in Bifurcation Theory: Volume I

Singularities and Groups in Bifurcation Theory: Volume I (Applied Mathematical Sciences, 51)

This book has been written in a frankly partisian spirit-we believe that singularity theory offers an extremely useful approach to bifurcation probÂ 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.
Country USA
Brand Springer
Manufacturer Springer
Binding Hardcover
ItemPartNumber 9780387909998
UnitCount 1
Format Illustrated
EANs 9780387909998
ReleaseDate 0000-00-00

Country	USA
Brand	Springer
Manufacturer	Springer
Binding	Hardcover
ItemPartNumber	9780387909998
UnitCount	1
Format	Illustrated
EANs	9780387909998
ReleaseDate	0000-00-00

Singularities and Groups in Bifurcation Theory: Volume I (Applied Mathematical Sciences, 51)

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