Topological Methods for Variational Problems with Symmetries
Seiten
1993
|
1993
Springer Berlin (Verlag)
978-3-540-57378-4 (ISBN)
Springer Berlin (Verlag)
978-3-540-57378-4 (ISBN)
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.
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.
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.
Erscheint lt. Verlag | 29.11.1993 |
---|---|
Reihe/Serie | Lecture Notes in Mathematics |
Zusatzinfo | X, 158 p. |
Verlagsort | Berlin |
Sprache | englisch |
Maße | 155 x 235 mm |
Gewicht | 264 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
Schlagworte | algebraic topology • Bifurcation Theory • critical point theory • Dynamical Systems • Equivariant topology • Minimum • Variational Problems |
ISBN-10 | 3-540-57378-X / 354057378X |
ISBN-13 | 978-3-540-57378-4 / 9783540573784 |
Zustand | Neuware |
Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Grundlagen, Beispiele, Aufgaben, Lösungen
Buch | Hardcover (2022)
Hanser, Carl (Verlag)
29,99 €