TOPICS IN BIFURCATION THEORY AND APPLICATIONS (Advanced Series in Nonlinear Dynamics) - Hardcover

Iooss, Gerard; Adelmeyer, Mortiz

Hardcover

ISBN 10: 9810210094 ISBN 13: 9789810210090

Publisher: World Scientific Pub Co Inc, 1992

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.

About this title

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

Edition details

• Publisher: World Scientific Pub Co Inc
• Publication date: 1992
• Language: English
• ISBN 10: 9810210094
• ISBN 13: 9789810210090
• Binding: Hardcover
• Number of pages: 168