Topological Methods for Variational Problems with Symmetries

Thomas Bartsch

ISBN 10: 354057378X / ISBN 13: 9783540573784

Published by Springer Berlin Heidelberg, J.B. Metzler Nov 1993, 1993

About this Item

This item is printed on demand - Print on Demand Titel. Neuware -Symmetry has a strong impact on the number and shape ofsolutions to variational problems. This has been observed, for instance, in the search for periodic solutions of Hamiltonian systems or of the nonlinear wave equation; when one is interested in elliptic equations on symmetric domains or in the corresponding semiflows; and when one is looking for 'special' solutions of these problems. This book is concerned with Lusternik-Schnirelmann theory and Morse-Conley theory for group invariant functionals. These topological methods are developed in detail with new calculations of the equivariant Lusternik-Schnirelmann category and versions of the Borsuk-Ulam theorem for very general classes of symmetry groups. The Morse-Conley theory is applied to bifurcation problems, in particular to the bifurcation of steady states and hetero-clinic orbits of O(3)-symmetric flows; and to the existence of periodic solutions nearequilibria of symmetric Hamiltonian systems. Some familiarity with the usualminimax theory and basic algebraic topology is assumed.Springer-Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 168 pp. Englisch.

Seller Inventory # 9783540573784

Bibliographic Details

• Title: Topological Methods for Variational Problems with Symmetries
• Publisher: Springer Berlin Heidelberg, J.B. Metzler Nov 1993
• Publication Date: 1993
• Language: English
• ISBN 10: 354057378X
• ISBN 13: 9783540573784
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 10D millimeters 235 millimeters width by 155 millimeters height by 10 millimeters depth
• Weight: 265 grams

About this title

Synopsis

Symmetry has a strong impact on the number and shape of solutions to variational problems. This has been observed, for instance, in the search for periodic solutions of Hamiltonian systems or of the nonlinear wave equation; when one is interested in elliptic equations on symmetric domains or in the corresponding semiflows; and when one is looking for "special" solutions of these problems. This book is concerned with Lusternik-Schnirelmann theory and Morse-Conley theory for group invariant functionals. These topological methods are developed in detail with new calculations of the equivariant Lusternik-Schnirelmann category and versions of the Borsuk-Ulam theorem for very general classes of symmetry groups. The Morse-Conley theory is applied to bifurcation problems, in particular to the bifurcation of steady states and hetero-clinic orbits of O(3)-symmetric flows; and to the existence of periodic solutions nearequilibria of symmetric Hamiltonian systems. Some familiarity with the usualminimax theory and basic algebraic topology is assumed.