Singularity Theory and Equivariant Symplectic Maps

This title is printed to order. This book may have been self-published. If so, we cannot guarantee the quality of the content. In the main most books will have gone through the editing process however some may not. We therefore suggest that you be aware of this before ordering this book. If in doubt check either the author or publisher’s details as we are unable to accept any returns unless they are faulty. Please contact us if you have any questions.

This monograph is a study of the local bifurcations of multiparameter symplectic maps of arbitrary dimension in the neighbourhood of a fixed point. The problem is reduced to a study of critical points of an equivariant gradient bifurcation problem, using the correspondence between orbits of a symplectic map and critical points of an action functional. New results on singularity theory for equivariant gradient bifurcation problems are obtained and then used to classify singularities of bifurcating period-q points. Of particular interest is the presentation of a general framework for analyzing group-theoretic aspects and singularities of symplectic maps (particularly period-q points). Topics include bifurcations when the symplectic map has spatial symmetry and a theory for the collision of multipliers near rational points with and without spatial symmetry. The monograph also includes 11 self-contained appendices each with a basic result on symplectic maps.