Local and semi-local bifurcations in Hamiltonian dynamical systems : results and examples / / Heinz Hanssmann

• Autore: Hanssmann Heinz
• Pubblicazione: Berlin, Germany : , : Springer, , [2007]; ©2007
• Edizione: 1st ed. 2007.
• Descrizione fisica: 1 online resource (XVI, 242 p. 22 illus.)
• Disciplina: 515.39
• Soggetto topico: Bifurcation theory; Hamiltonian systems
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references (pages [219]-233) and index.
• Nota di contenuto: 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.
• Sommario/riassunto: 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.
• Titolo autorizzato: Local and semi-local bifurcations in Hamiltonian dynamical systems
• ISBN: 3-540-38896-6
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910483362203321
• Lo trovi qui: Univ. Federico II
• Serie: Lecture Notes in Mathematics, . 0075-8434 ; ; 1893