Singularity theory and equivariant symplectic maps. Lecture notes in mathematics ; 1558

Bridges, Thomas J. und Jacques E. Furter,

ISBN 10: 3540572961 / ISBN 13: 9783540572961

Published by Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo ; Hong Kong ; Barcelona ; Budapest : Springer, 1993

About this Item

VI, 226 pages: graph. Darst. Ex-Library book in good condition. 9783540572961 Sprache: Englisch Gewicht in Gramm: 550.

Seller Inventory # 1160048

Bibliographic Details

• Title: Singularity theory and equivariant symplectic maps. Lecture notes in mathematics ; 1558
• Publisher: Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo ; Hong Kong ; Barcelona ; Budapest : Springer
• Publication Date: 1993
• Language: English
• ISBN 10: 3540572961
• ISBN 13: 9783540572961
• Binding: Soft cover
• Seller catalogs:
  • SA MATHEMATIK

About this title

Synopsis

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.