LEADER 04417nam 22008055 450 001 9910484477503321 005 20200702095155.0 010 $a9786610937141 010 $a9781280937149 010 $a1280937149 010 $a9783540724704 010 $a3540724702 024 7 $a10.1007/978-3-540-72470-4 035 $a(CKB)1000000000437259 035 $a(EBL)3037348 035 $a(SSID)ssj0000166964 035 $a(PQKBManifestationID)11161940 035 $a(PQKBTitleCode)TC0000166964 035 $a(PQKBWorkID)10169779 035 $a(PQKB)10658583 035 $a(DE-He213)978-3-540-72470-4 035 $a(MiAaPQ)EBC3037348 035 $a(MiAaPQ)EBC6281430 035 $a(PPN)123162270 035 $a(EXLCZ)991000000000437259 100 $a20100301d2007 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aHamiltonian Reduction by Stages /$fby Jerrold E. Marsden, Gerard Misiolek, Juan-Pablo Ortega, Matthew Perlmutter, Tudor S. Ratiu 205 $a1st ed. 2007. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2007. 215 $a1 online resource (526 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1913 300 $aDescription based upon print version of record. 311 08$a9783540724698 311 08$a3540724699 320 $aIncludes bibliographical references (pages [483]-508) and index. 327 $aBackground and the Problem Setting -- Symplectic Reduction -- Cotangent Bundle Reduction -- The Problem Setting -- Regular Symplectic Reduction by Stages -- Commuting Reduction and Semidirect Product Theory -- Regular Reduction by Stages -- Group Extensions and the Stages Hypothesis -- Magnetic Cotangent Bundle Reduction -- Stages and Coadjoint Orbits of Central Extensions -- Examples -- Stages and Semidirect Products with Cocycles -- Reduction by Stages via Symplectic Distributions -- Reduction by Stages with Topological Conditions -- Optimal Reduction and Singular Reduction by Stages, by Juan-Pablo Ortega -- The Optimal Momentum Map and Point Reduction -- Optimal Orbit Reduction -- Optimal Reduction by Stages. 330 $aIn this volume readers will find for the first time a detailed account of the theory of symplectic reduction by stages, along with numerous illustrations of the theory. Special emphasis is given to group extensions, including a detailed discussion of the Euclidean group, the oscillator group, the Bott-Virasoro group and other groups of matrices. Ample background theory on symplectic reduction and cotangent bundle reduction in particular is provided. Novel features of the book are the inclusion of a systematic treatment of the cotangent bundle case, including the identification of cocycles with magnetic terms, as well as the general theory of singular reduction by stages. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1913 606 $aDynamics 606 $aErgodic theory 606 $aGeometry, Differential 606 $aMathematical physics 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 606 $aTheoretical, Mathematical and Computational Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19005 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aGeometry, Differential. 615 0$aMathematical physics. 615 14$aDynamical Systems and Ergodic Theory. 615 24$aDifferential Geometry. 615 24$aTheoretical, Mathematical and Computational Physics. 676 $a514/.74 700 $aMarsden$b Jerrold E$4aut$4http://id.loc.gov/vocabulary/relators/aut$07790 702 $aMisiolek$b Gerard$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aOrtega$b Juan-Pablo$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aPerlmutter$b Matthew$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aRatiu$b Tudor S$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910484477503321 996 $aHamiltonian reduction by stages$91020474 997 $aUNINA