Topics in bifurcation theory and applications

著者

• Iooss, Gérard
• Adelmeyer, Moritz

書誌事項

Topics in bifurcation theory and applications

Gérard Iooss, Moritz Adelmeyer

（Advanced series in nonlinear dynamics, v. 3）

World Scientific, c1998

2nd ed

注記

Includes bibliographical references (p. 183-186)

内容説明・目次

内容説明

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.

目次

• Centre manifolds normal forms, and bifurcations of vector
• fields near critical points - unperturbed vector fields
• perturbed vector fields
• Couette-Taylor problem - formulation of the problem
• Couette flow
• bifurcations from Couette flow
• bifurcations from Taylor vortex flow
• centre manifolds, normal forms, and bifurcations of vector
• fields near closed orbits - preliminaries
• adaptation of Floquet thoery
• unperturbed case
• perturbed case.

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詳細情報

• NII書誌ID(NCID): BA40945654
• ISBN:
  • 9810237286
• 出版国コード: si
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Singapore ; River Edge, N.J.
• ページ数/冊数: viii, 186 p.
• 大きさ: 23 cm
• 分類:
  • LCC : QA380
  • DC20 : 515/.35
• 件名:
  • LCSH : Bifurcation theory
  • FREE : 分岐理論
• 親書誌ID:
  • BA12210467