Bifurcations in Hydrodynamic Stability Problems
The work of Lorenz 1963 and of Ruelle and Takens 1971 initiated the introduction into hydrodynamic stability theory of concepts and principles from the currently active mathematical field of topological dynamical systems. It was immediately clear that some of the concepts, for example the concept of generic properties of systems, have many applications elsewhere in physics. Also the new concepts and principles put new light on old things, such as bifurcation phenomena. The idea of strange attractors and their connection with continuous power spectra gave a new understanding of chaotic behavior generally.
KeywordsEquation of evolution Navier-Stokes equation Poiseuille and Couette problems Taylor vortices wavy vortices flows and semiflows in a Hilbert space normal modes completeness of the normal mode system invariant manifolds stable and unstable manifolds fixed points closed orbits and invariant tori bifurcation supercritical and subcritical bifurcation subharmonic bifurcation Poincaré mappings
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