000 03388nam a22005055i 4500
001 978-3-540-48099-0
003 DE-He213
005 20190213151323.0
007 cr nn 008mamaa
008 121227s1993 gw | s |||| 0|eng d
020 _a9783540480990
_9978-3-540-48099-0
024 7 _a10.1007/BFb0073859
_2doi
050 4 _aQA612-612.8
072 7 _aPBPD
_2bicssc
072 7 _aMAT038000
_2bisacsh
072 7 _aPBPD
_2thema
082 0 4 _a514.2
_223
100 1 _aBartsch, Thomas.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aTopological Methods for Variational Problems with Symmetries
_h[electronic resource] /
_cby Thomas Bartsch.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1993.
300 _aX, 158 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1560
505 0 _aCategory, 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.
520 _aSymmetry 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.
650 0 _aAlgebraic topology.
650 0 _aGlobal analysis (Mathematics).
650 0 _aCell aggregation
_xMathematics.
650 1 4 _aAlgebraic Topology.
_0http://scigraph.springernature.com/things/product-market-codes/M28019
650 2 4 _aAnalysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12007
650 2 4 _aManifolds and Cell Complexes (incl. Diff.Topology).
_0http://scigraph.springernature.com/things/product-market-codes/M28027
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662178522
776 0 8 _iPrinted edition:
_z9783540573784
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1560
856 4 0 _uhttps://doi.org/10.1007/BFb0073859
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c10266
_d10266