Lecture Notes in Mathematics

1 primary work

Singularity Theory and Equivariant Symplectic Maps

by Thomas J Bridges and Jacques E. Furter

Published 29 November 1993

The monograph is a study of the local bifurcations of
multiparameter symplectic maps of arbitrary dimension in the
neighborhood 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
ofa symplectic map and critical points of an action
functional. New results onsingularity theory for
equivariant gradient bifurcation problems are obtained and
then used to classify singularities of bifurcating period-q
points. Of particular interest is that a general framework
for analyzing group-theoretic aspects and singularities of
symplectic maps (particularly period-q points) is presented.
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. The
monograph will appeal to researchers and graduate students
in the areas of symplectic maps, Hamiltonian systems,
singularity theory and equivariant bifurcation theory.