Topics in bifurcation theory and applications. Advanced series in nonlinear dynamics 3 ED.2.

Iooss, Gerard; Adelmeyer, Moritz

ISBN 10: 9810237286 / ISBN 13: 9789810237288

Published by Singapore , World Scientific, 1999

About this Item

Ex-library with stamp and library-signature. GOOD condition, some traces of use. Ancien Exemplaire de bibliothèque avec signature et cachet. BON état, quelques traces d'usure. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. 34 IOO 9789810237288 Sprache: Englisch Gewicht in Gramm: 550.

Seller Inventory # 2498837

Bibliographic Details

• Title: Topics in bifurcation theory and applications. Advanced series in nonlinear dynamics 3 ED.2.
• Publisher: Singapore , World Scientific
• Publication Date: 1999
• Language: English
• ISBN 10: 9810237286
• ISBN 13: 9789810237288
• Binding: Hardcover
• Edition: 2nd Edition
• Weight: 550 grams
• Seller catalogs:
  • SA MATHEMATIK

About this title

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.