Topological Methods for Variational Problems with Symmetries: 1560 - Brossura

Bartsch, Thomas

Brossura

ISBN 10: 354057378X ISBN 13: 9783540573784

Casa editrice: Springer, 2009

Riassunto

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.

Su questo libro

Contenuti

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.

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 2009
• Lingua: Inglese
• ISBN 10: 354057378X
• ISBN 13: 9783540573784
• Rilegatura: Copertina flessibile
• Numero di pagine: 168
• Contatto del produttore: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Germania