LEADER 02848nam 2200589 450 001 996466626003316 005 20220506131316.0 010 $a3-540-38896-6 024 7 $a10.1007/3-540-38894-X 035 $a(CKB)1000000000282856 035 $a(SSID)ssj0000193702 035 $a(PQKBManifestationID)11937226 035 $a(PQKBTitleCode)TC0000193702 035 $a(PQKBWorkID)10226442 035 $a(PQKB)11077103 035 $a(DE-He213)978-3-540-38896-8 035 $a(MiAaPQ)EBC4643116 035 $a(MiAaPQ)EBC6706193 035 $a(Au-PeEL)EBL6706193 035 $a(PPN)123156815 035 $a(EXLCZ)991000000000282856 100 $a20220506d2007 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aLocal and semi-local bifurcations in Hamiltonian dynamical systems $eresults and examples /$fHeinz Hanssmann 205 $a1st ed. 2007. 210 1$aBerlin, Germany :$cSpringer,$d[2007] 210 4$dİ2007 215 $a1 online resource (XVI, 242 p. 22 illus.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1893 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-38894-X 320 $aIncludes bibliographical references (pages [219]-233) and index. 327 $aBifurcations of Equilibria -- Bifurcations of Periodic Orbits -- Bifurcations of Invariant Tori -- Perturbations of Ramified Torus Bundles -- Planar Singularities -- Stratifications -- Normal Form Theory -- Proof of the Main KAM Theorem -- Proofs of the Necessary Lemmata. 330 $aOnce again KAM theory is committed in the context of nearly integrable Hamiltonian systems. While elliptic and hyperbolic tori determine the distribution of maximal invariant tori, they themselves form n-parameter families. Hence, without the need for untypical conditions or external parameters, torus bifurcations of high co-dimension may be found in a single given Hamiltonian system. The text moves gradually from the integrable case, in which symmetries allow for reduction to bifurcating equilibria, to non-integrability, where smooth parametrisations have to be replaced by Cantor sets. Planar singularities and their versal unfoldings are an important ingredient that helps to explain the underlying dynamics in a transparent way. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1893 606 $aBifurcation theory 606 $aHamiltonian systems 615 0$aBifurcation theory. 615 0$aHamiltonian systems. 676 $a515.39 700 $aHanssmann$b Heinz$0296288 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466626003316 996 $aLocal and semi-local bifurcations in Hamiltonian dynamical systems$9230553 997 $aUNISA