Singularity Theory and Equivariant Symplectic Maps

1993
ISBN: 978-3-540-57296-1
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1558, 230 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 365 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Furter, Jacques E.

Bridges, Thomas J.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie

Inhaltsverzeichnis

Generic bifurcation of periodic points.- Singularity theory for equivariant gradient bifurcation problems.- Classification of Zq-equivariant gradient bifurcation problems.- Period-3 points of the generalized standard map.- Classification of Dq-equivariant gradient bifurcation problems.- Reversibility and degenerate bifurcation of period-q points of multiparameter maps.- Periodic points of equivariant symplectic maps.- Collision of multipliers at rational points for symplectic maps.- Equivariant maps and the collision of multipliers.