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.

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Bibliographic Information

Book Title: Singularity Theory and Equivariant Symplectic Maps
Authors: Thomas J. Bridges, Jacques E. Furter
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/BFb0073471
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1993
Softcover ISBN: 978-3-540-57296-1Published: 29 November 1993
eBook ISBN: 978-3-540-48040-2Published: 15 November 2006
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: VI, 230
Topics: Manifolds and Cell Complexes (incl. Diff.Topology), Analysis

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Table of contents (10 chapters)

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