Topics in bifurcation theory and applications
Author(s)
Bibliographic Information
Topics in bifurcation theory and applications
（Advanced series in nonlinear dynamics, v. 3）
World Scientific, c1992
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Note
Includes bibliographical references (p. 157-160)
Description and Table of Contents
Description
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.
Table of Contents
- Part 1 Center manifolds, normal forms, and bifurcations of vector fields near critical points: unperturbed vector fields. Part 2 Couette-Taylor problem: formulation of the problem
- Couette flow
- bifurcations from Couette flow
- bifurcations form taylor vortex flow. Part 3 Center manifolds, normal forms and bifurcations of vector fields near closed orbits: preliminaries, adaptation and Floquet theory
- unperturbed case, perturbed case.
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