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Elementary stability and bifurcation theory
Asymptotic solutions of evolution problems bifurcation and stability of steady solutions of evolution equations in one dimension imperfection theory and isolated solutions which perturb bifurcationExpand
Topics in bifurcation theory and applications
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 CouetteExpand
A simple global characterization for normal forms of singular vector fields
We derive a new global characterization of the normal forms of amplitude equations describing the dynamics of competing order parameters in degenerate bifurcation problems. Using an appropriateExpand
Center Manifold Theory in Infinite Dimensions
Center manifold theory forms one of the cornerstones of the theory of dynamical systems. This is already true for finite-dimensional systems, but it holds a fortiori in the infinite-dimensional case.Expand
Perturbed Homoclinic Solutions in Reversible 1:1 Resonance Vector Fields
We consider a smooth reversible vector field in R^4, such that the origin is a fixed point. The differential at the origin has two double pure imaginary eigenvalues ±iq for the critical value 0 ofExpand
The Couette-Taylor Problem
This monograph presents a systematic and unified approach to the non-linear stability problem and transitions in the Couette-Taylor problem, by the means of analytic and constructive methods. TheExpand
Local Bifurcations, Center Manifolds, and Normal Forms in Infinite-Dimensional Dynamical Systems
This book is an extension of different lectures given by the authors during many years at the University of Nice, at the University of Stuttgart in 1990, and the Uni- versity of Bordeaux in 2000Expand
Standing Waves on an Infinitely Deep Perfect Fluid Under Gravity
The existence of two-dimensional standing waves on the surface of an infinitely deep perfect fluid under gravity is established. When formulated as a second-order equation for a real-valued functionExpand