LEADER 03294nam 2200613 450 001 996466758703316 005 20220304170143.0 010 $a3-540-46441-7 024 7 $a10.1007/BFb0097544 035 $a(CKB)1000000000437089 035 $a(SSID)ssj0000323697 035 $a(PQKBManifestationID)12064874 035 $a(PQKBTitleCode)TC0000323697 035 $a(PQKBWorkID)10303326 035 $a(PQKB)10254010 035 $a(DE-He213)978-3-540-46441-9 035 $a(MiAaPQ)EBC5595517 035 $a(Au-PeEL)EBL5595517 035 $a(OCoLC)1076232198 035 $a(MiAaPQ)EBC6842695 035 $a(Au-PeEL)EBL6842695 035 $a(OCoLC)793079267 035 $a(PPN)155207059 035 $a(EXLCZ)991000000000437089 100 $a20220304d1991 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aHamiltonian and lagrangian flows on center manifolds $ewith applications to elliptic variational problems /$fAlexander Mielke 205 $a1st ed. 1991. 210 1$aBerlin :$cSpringer,$d[1991] 210 4$dİ1991 215 $a1 online resource (X, 140 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1489 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-54710-X 327 $aNotations and basic facts on center manifolds -- The linear theory -- Hamiltonian flows on center manifolds -- Hamiltonian systems with symmetries -- Lagrangian systems -- Nonautonomous systems -- Elliptic variational problems on cylindrical domains -- Capillarity surface waves -- Necking of strips -- Saint-Venant's problem. 330 $aThe theory of center manifold reduction is studied in this monograph in the context of (infinite-dimensional) Hamil- tonian and Lagrangian systems. The aim is to establish a "natural reduction method" for Lagrangian systems to their center manifolds. Nonautonomous problems are considered as well assystems invariant under the action of a Lie group ( including the case of relative equilibria). The theory is applied to elliptic variational problemson cylindrical domains. As a result, all bounded solutions bifurcating from a trivial state can be described by a reduced finite-dimensional variational problem of Lagrangian type. This provides a rigorous justification of rod theory from fully nonlinear three-dimensional elasticity. The book will be of interest to researchers working in classical mechanics, dynamical systems, elliptic variational problems, and continuum mechanics. It begins with the elements of Hamiltonian theory and center manifold reduction in order to make the methods accessible to non-specialists, from graduate student level. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1489 606 $aCalculus of variations$xData processing 606 $aDifferential equations, Elliptic 615 0$aCalculus of variations$xData processing. 615 0$aDifferential equations, Elliptic. 676 $a515.64 700 $aMielke$b Alexander$f1958-$0315674 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466758703316 996 $aHamiltonian and Lagrangian flows on center manifolds$978594 997 $aUNISA