Singularity Theory and Equivariant Symplectic Maps / by Thomas J. Bridges, Jacques E. Furter.

Format:

Book

Author/Creator:

Bridges, Thomas J., 1955- author.

Furter, Jacques E., 1957- author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1558.

Lecture Notes in Mathematics, 0075-8434 ; 1558

Language:

English

Subjects (All):

Cell aggregation--Mathematics.

Cell aggregation.

Global analysis (Mathematics).

Manifolds and Cell Complexes (incl. Diff.Topology).

Analysis.

Local Subjects:

Manifolds and Cell Complexes (incl. Diff.Topology).

Analysis.

Physical Description:

1 online resource (VI, 230 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1993.

System Details:

text file PDF

Summary:

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.

Contents:

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.

Other Format:

Printed edition:

ISBN:

9783540480402

Access Restriction:

Restricted for use by site license.