Topics In Bifurcation Theory And Applications (2nd Edition): 3 (Advanced Series in Nonlinear Dynamics) - Hardcover

Adelmeyer, Moritz; Iooss, Gerard

Hardcover

ISBN 10: 9810237286 ISBN 13: 9789810237288

Publisher: World Scientific Publishing Co Pte Ltd, 1999

Synopsis

This textbook presents the most efficient analytical techniques in the local bifurcation theory of vector fields. It is centered on the theory of normal forms and its applications, including interaction with symmetries.The first part of the book reviews the center manifold reduction and introduces normal forms (with complete proofs). Basic bifurcations are studied together with bifurcations in the presence of symmetries. Special attention is given to examples with reversible vector fields, including the physical example given by the water waves. In this second edition, many problems with detailed solutions are added at the end of the first part (some systems being in infinite dimensions). The second part deals with the Couette-Taylor hydrodynamical stability problem, between concentric rotating cylinders. The spatial structure of various steady or unsteady solutions results directly from the analysis of the reduced system on a center manifold. In this part we also study bifurcations (simple here) from group orbits of solutions in an elementary way (avoiding heavy algebra). The third part analyzes bifurcations from time periodic solutions of autonomous vector fields. A normal form theory is developed, covering all cases, and emphasizing a partial Floquet reduction theory, which is applicable in infinite dimensions. Studies of period doubling as well as Arnold's resonance tongues are included in this part.

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

Synopsis

This textbook presents efficient analytical techniques in the local bifurcation theory of vector fields. It is centred on the theory of normal forms and its applications, including interactions with symmetries. Attention is given to examples with reversible vector fields, including the physical example given by the water waves. The second part deals with the Couette-Taylor hydrodynamical stability problem, between concentric rotating cylinders. The spatial structure of various steady or unsteady solutions is covered. The text also studies bifurcations from group orbits of solutions in an elementary way. The third part analyzes bifurcations from time periodic solutions of autonomous vector fields. A normal form theory is developed, covering all cases, and emphasizing a partial Floquet reduction theory, which is applicable in infinite dimensions. Studies of period doubling as well as Arnold's resonance tongues are included in this part.

Edition details

• Publisher: World Scientific Publishing Co Pte Ltd
• Publication date: 1999
• Language: English
• ISBN 10: 9810237286
• ISBN 13: 9789810237288
• Binding: Hardcover
• Edition number: 2
• Number of pages: 196