E-Book, Englisch, Band 1560, 158 Seiten, eBook
Reihe: Lecture Notes in Mathematics
E-Book, Englisch, Band 1560, 158 Seiten, eBook
Reihe: Lecture Notes in Mathematics
ISBN: 978-3-540-48099-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.
Weitere Infos & Material
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.
