Topological Methods for Variational Problems with Symmetries

1993
ISBN: 978-3-540-57378-4
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1560, 158 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 265 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Bartsch, Thomas

Fachgebiete

• Mathematik | Informatik Mathematik Topologie
• Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung

Inhaltsverzeichnis

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.