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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 bifurcation… Expand

Topics in bifurcation theory and applications

- G. Iooss, Moritz Adelmeyer
- Mathematics
- 25 January 1999

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… Expand

A simple global characterization for normal forms of singular vector fields

- C. Elphick, E. Tirapegui, M. Brachet, P. Coullet, G. Iooss
- Mathematics
- 1 November 1987

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 appropriate… Expand

Center Manifold Theory in Infinite Dimensions

- A. Vanderbauwhede, G. Iooss
- Mathematics
- 1992

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

- G. Iooss, Marie-Christine Pérouème
- Mathematics
- 1 March 1993

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 of… Expand

The Couette-Taylor Problem

- P. Chossat, G. Iooss
- Mathematics
- 1992

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. The… Expand

Water waves for small surface tension : an approach via normal form

- G. Iooss, K. Kirchgässner
- Mathematics
- 1992

Local Bifurcations, Center Manifolds, and Normal Forms in Infinite-Dimensional Dynamical Systems

- M. Haragus, G. Iooss
- Mathematics, Physics
- 8 December 2010

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 2000… Expand

Standing Waves on an Infinitely Deep Perfect Fluid Under Gravity

- G. Iooss, P. Plotnikov, J. Toland
- Mathematics
- 11 June 2005

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 function… Expand

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