Topics in Bifurcation Theory and Applications (Advanced Series in Nonlinear Dynamics)

Iooss, Gerard, Adelmeyer, Mortiz

ISBN 10: 9810210094 / ISBN 13: 9789810210090

Published by World Scientific Pub Co Inc, 1992

About this Item

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Seller Inventory # ERICA82998102100943

Bibliographic Details

• Title: Topics in Bifurcation Theory and Applications (Advanced Series in Nonlinear Dynamics)
• Publisher: World Scientific Pub Co Inc
• Publication Date: 1992
• Language: English
• ISBN 10: 9810210094
• ISBN 13: 9789810210090
• Binding: Hardcover
• Condition: Very Good
• Dust Jacket Condition: Dust Jacket Included
• Book Type: book

About this title

Synopsis

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.

Review

"The book is very well written, and the many examples make it an excellent choice for an (intermediate) course on bifurcation problems." Mathematics Abstracts