What's it all about? -- Families of functions -- The ring of germs of smooth functions -- Right equivalence -- Finite determinacy -- Classification of the elementary catastrophes -- Unfoldings & catastrophes -- Singularities of plane curves -- Even functions -- Families of maps and bifurcations -- Contact equivalence -- Tangent spaces -- Classification for contact equivalence -- Contact equivalence and unfoldings -- Geometric applications -- Preparation theorem -- Left-right equivalence -- Bifurcation problems and paths -- Vector fields tangent to a variety -- Kv-equivalence -- Classification of paths -- Loose ends -- Constrained bifurcation problems.
Summary:
"Suitable for advanced undergraduates, postgraduates and researchers, this self-contained textbook provides an introduction to the mathematics lying at the foundations of bifurcation theory. The theory is built up gradually, beginning with the well-developed approach to singularity theory through right-equivalence. The text proceeds with contact equivalence of map-germs and finally presents the path formulation of bifurcation theory. This formulation, developed partly by the author, is more general and more flexible than the original one dating from the 1980s. A series of appendices discuss standard background material, such as calculus of several variables, existence and uniqueness theorems for ODEs, and some basic material on rings and modules. Based on the author's own teaching experience, the book contains numerous examples and illustrations. The wealth of end-of-chapter problems develop and reinforce understanding of the key ideas and techniques: solutions to a selection are provided"-- Provided by publisher.
This resource is supported by the Institute of Museum and Library Services under the provisions of the Library Services and Technology Act as administered by State Library of Iowa.