Geometry - Euclidean & Projective, Mathematics - Topology, Mathematics - Fields, Vectors & Tensors
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Overview
This book examines qualitative properties of vector fields in the plane, in the spirit of Hilbert's Sixteenth Problem. Two principal topics explored are bifurcations of limit cycles of planar vector fields and desingularization of singular points for individual vector fields and for analytic families of such fields. In addition to presenting important new developments in this area, this book contains an introductory paper which outlines the general context and describes connections between the papers in the volume. The book will appeal to researchers and graduate students working in the qualitative theory of ordinary differential equations and dynamical systems.
Editorials
Booknews
Six papers consider qualitative properties of vector fields on the plane, particularly bifurcations of limit cycles of planar vector fields and the desingularization of singular points for individual vector fields and for analytic families of such fields. An introduction to Hilbert's sixteenth problem is followed by discussions of the finite cyclicity of elementary polycycles in generic families, desingularization in families of analytic differential equations, the order of the topologically sufficient jet of a smooth vector field on the real plane at a singular point of finite multiplicity, few-parameter generic families of vector fields on the two-dimensional sphere, and geometric proof of the Bautin theorem. No index. Annotation c. Book News, Inc., Portland, OR (booknews.com)Book Details
Published
August 3, 1995
Publisher
American Mathematical Society
Pages
219
Format
Hardcover
ISBN
9780821803622