02850nam 2200589 450 991048336220332120220506131316.03-540-38896-610.1007/3-540-38894-X(CKB)1000000000282856(SSID)ssj0000193702(PQKBManifestationID)11937226(PQKBTitleCode)TC0000193702(PQKBWorkID)10226442(PQKB)11077103(DE-He213)978-3-540-38896-8(MiAaPQ)EBC4643116(MiAaPQ)EBC6706193(Au-PeEL)EBL6706193(PPN)123156815(EXLCZ)99100000000028285620220506d2007 uy 0engurnn#008mamaatxtccrLocal and semi-local bifurcations in Hamiltonian dynamical systems results and examples /Heinz Hanssmann1st ed. 2007.Berlin, Germany :Springer,[2007]©20071 online resource (XVI, 242 p. 22 illus.)Lecture Notes in Mathematics,0075-8434 ;1893Bibliographic Level Mode of Issuance: Monograph3-540-38894-X Includes bibliographical references (pages [219]-233) and index.Bifurcations 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.Once 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.Lecture Notes in Mathematics,0075-8434 ;1893Bifurcation theoryHamiltonian systemsBifurcation theory.Hamiltonian systems.515.39Hanssmann Heinz296288MiAaPQMiAaPQMiAaPQBOOK9910483362203321Local and semi-local bifurcations in Hamiltonian dynamical systems230553UNINA