# Singularity Theory and Equivariant Symplectic Maps

Part of the Lecture Notes in Mathematics book series (LNM, volume 1558)

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Part of the Lecture Notes in Mathematics book series (LNM, volume 1558)

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.

Area Hamiltonian systems bifurcation classification framework function functional hamiltonian system singularity singularity theory symmetry symplectic maps

- DOI https://doi.org/10.1007/BFb0073471
- Copyright Information Springer-Verlag Berlin Heidelberg 1993
- Publisher Name Springer, Berlin, Heidelberg
- eBook Packages Springer Book Archive
- Print ISBN 978-3-540-57296-1
- Online ISBN 978-3-540-48040-2
- Series Print ISSN 0075-8434
- Series Online ISSN 1617-9692
- Buy this book on publisher's site

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