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＜電子ブック＞
Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems : Results and Examples / by Heinz Hanßmann
(Lecture Notes in Mathematics. ISSN:16179692 ; 1893)

版	1st ed. 2007.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2007
本文言語	英語
大きさ	XVI, 242 p. 22 illus : online resource
著者標目	*Hanßmann, Heinz author SpringerLink (Online service)
件　名	LCSH:Dynamical systems LCSH:Differential equations LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Mathematical physics FREE:Dynamical Systems FREE:Differential Equations FREE:Global Analysis and Analysis on Manifolds FREE:Theoretical, Mathematical and Computational Physics
一般注記	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 HTTP:URL=https://doi.org/10.1007/3-540-38894-X

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