Thomas Bartsch

Topological Methods for Variational Problems with Symmetries

• Broschiertes Buch

Produktbeschreibung

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 ofHamiltonian systems or of the nonlinear wave equation; whenone is interested in elliptic equations on symmetric domainsor in the corresponding semiflows; and when one is lookingfor "special" solutions of these problems.This book is concerned with Lusternik-Schnirelmann theoryand Morse-Conley theory for group invariant functionals.These topological methods are developed in detail with newcalculations of the equivariant Lusternik-Schnirelmanncategory and versions of the Borsuk-Ulam theorem for verygeneral classes of symmetry groups. The Morse-Conley theoryis applied to bifurcation problems, in particular to thebifurcation of steady states and hetero-clinic orbits ofO(3)-symmetric flows; and to the existence of periodicsolutions nearequilibria of symmetric Hamiltonian systems.Some familiarity with the usualminimax theory and basicalgebraic topology is assumed.

Produktdetails

• Lecture Notes in Mathematics 1560
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-540-57378-4
• 1993
• Seitenzahl: 168
• Erscheinungstermin: 29. November 1993
• Englisch
• Abmessung: 235mm x 155mm x 10mm
• Gewicht: 264g
• ISBN-13: 9783540573784
• ISBN-10: 354057378X
• Artikelnr.: 23888878

Autorenporträt

Dr. Thomas Bartsch promovierte bei Prof. Dr. A. Drexl am Institut für Betriebswirtschaftslehre der Universität Kiel. Er ist als Software-Entwickler bei der SAP AG in Walldorf tätig.

Inhaltsangabe

Category, genus and critical point theory with symmetries.- Category and genus of infinite-dimensional representation spheres.- The length of G-spaces.- The length of representation spheres.- The length and Conley index theory.- The exit-length.- Bifurcation for O(3)-equivariant problems.- Multiple periodic solutions near equilibria of symmetric Hamiltonian systems.