LEADER 03473nam 22006255 450 001 9910146312703321 005 20250730104742.0 010 $a3-540-48073-0 024 7 $a10.1007/BFb0094677 035 $a(CKB)1000000000437294 035 $a(SSID)ssj0000325600 035 $a(PQKBManifestationID)12068807 035 $a(PQKBTitleCode)TC0000325600 035 $a(PQKBWorkID)10325091 035 $a(PQKB)11513190 035 $a(DE-He213)978-3-540-48073-0 035 $a(MiAaPQ)EBC5577464 035 $a(Au-PeEL)EBL5577464 035 $a(OCoLC)1066182046 035 $a(MiAaPQ)EBC6853125 035 $a(Au-PeEL)EBL6853125 035 $a(PPN)155216244 035 $a(EXLCZ)991000000000437294 100 $a20121227d1999 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aPeriodic Solutions of the N-Body Problem /$fby Kenneth R. Meyer 205 $a1st ed. 1999. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d1999. 215 $a1 online resource (XIV, 154 p.) 225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v1719 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a3-540-66630-3 327 $aEquations of celestial mechanics -- Hamiltonian systems -- Central configurations -- Symmetries, integrals, and reduction -- Theory of periodic solutions -- Satellite orbits -- The restricted problem -- Lunar orbits -- Comet orbits -- Hill?s lunar equations -- The elliptic problem. 330 $aThe N-body problem is the classical prototype of a Hamiltonian system with a large symmetry group and many first integrals. These lecture notes are an introduction to the theory of periodic solutions of such Hamiltonian systems. From a generic point of view the N-body problem is highly degenerate. It is invariant under the symmetry group of Euclidean motions and admits linear momentum, angular momentum and energy as integrals. Therefore, the integrals and symmetries must be confronted head on, which leads to the definition of the reduced space where all the known integrals and symmetries have been eliminated. It is on the reduced space that one can hope for a nonsingular Jacobian without imposing extra symmetries. These lecture notes are intended for graduate students and researchers in mathematics or celestial mechanics with some knowledge of the theory of ODE or dynamical system theory. The first six chapters develops the theory of Hamiltonian systems, symplectic transformations and coordinates, periodic solutions and their multipliers, symplectic scaling, the reduced space etc. The remaining six chapters contain theorems which establish the existence of periodic solutions of the N-body problem on the reduced space. 410 0$aLecture Notes in Mathematics,$x1617-9692 ;$v1719 606 $aGlobal analysis (Mathematics) 606 $aManifolds (Mathematics) 606 $aGlobal Analysis and Analysis on Manifolds 615 0$aGlobal analysis (Mathematics) 615 0$aManifolds (Mathematics) 615 14$aGlobal Analysis and Analysis on Manifolds. 676 $a514.74 686 $a58F05$2msc 700 $aMeyer$b Kenneth R$g(Kenneth Ray),$f1937-$059481 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910146312703321 996 $aPeriodic solutions of the N-body problem$978790 997 $aUNINA