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

Elementary Bifurcations.- Center Manifolds.- Normal Forms.- Reversible Bifurcations.- Applications.- Appendix.

From the reviews:

'This book relies on versions of the center manifold theorem that apply to infinite-dimensional dynamical systems...Chapter 4 of the book is distinctive in its presentation of normal forms for bifurcations in 'reversible' systems. These are systems in which there is a symmetry that reverses the orientation of time. When this symmetry is a reflection, it leads to systems that have large families of periodic orbits because forward and backward trajectories that start on the subspace must meet if they return to this subspace. This is an intricate subject, and this book makes it much more accessible than ever before. As for much of Iooss' work throughout his career, this book gives many concrete examples of problems described by PDEs with an excellent balance between theory and applications of that theory' (SIAM Review, December 2011)

"This book relies on versions of the center manifold theorem that apply to infinite-dimensional dynamical systems. ... This is an intricate subject, and this book makes it much more accessible than ever before. As for much of Iooss' work throughout his career, this book gives many concrete examples of problems described by PDEs with an excellent balance between theory and applications of that theory." (John Guckenheimer, SIAM Review, Vol. 53 (4), 2011)