
Topics In Bifurcation Theory And Applications
World Scientific Publishing Co Pte Ltd
Will be published approx. on 1. May 1992
Book
Hardback
168 pages
978-981-02-1009-0 (ISBN)
Description
This textbook presents modern techniques of local bifurcation theory of vector fields. The first part reviews the Center Manifold theory and introduces a constructive approach of Normal Forms, with many examples. Basic bifurcations as saddle-node, pitchfork and Hopf are studied, together with bifurcations in the presence of symmetries. Special attention is given to examples with reversible vector fields. The second part deals with the Couette-Taylor hydrodynamical instability problem, between concentric rotating cylinders, when the rotation rates are varied. Primary bifurcations to Taylor-vortex flow, Spirals and Ribbons are studied, and secondary bifurcations are presented as illustrations of bifurcations from group orbits of solutions. The third part analyses bifurcations from periodic solutions, i.e. perturbations of an autonomous vector field having a closed orbit. Same tools are used, and studies of period doubling as well as Arnold's resonance tongues are included.
Reviews / Votes
"The book is very well written, and the many examples make it an excellent choice for an (intermediate) course on bifurcation problems." Mathematics AbstractsMore details
Series
Language
English
Place of publication
Singapore
Singapore
Target group
College/higher education
Professional and scholarly
ISBN-13
978-981-02-1009-0 (9789810210090)
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Schweitzer Classification
Persons
Content
Part 1 Center manifolds, normal forms, and bifurcations of vector fields near critical points: unperturbed vector fields. Part 2 Couette-Taylor problem: formulation of the problem; Couette flow; bifurcations from Couette flow; bifurcations form taylor vortex flow. Part 3 Center manifolds, normal forms and bifurcations of vector fields near closed orbits: preliminaries, adaptation and Floquet theory; unperturbed case, perturbed case.