Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems

Results and Examples
1. Auflage 2006
ISBN: 978-3-540-38894-4
Verlag: Springer

Buch, Englisch, Band 1893, 242 Seiten, Book w. online files / update, Format (B × H): 155 mm x 235 mm, Gewicht: 409 g

Reihe: Lecture Notes in Mathematics

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 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.

Zielgruppe

Research

Autoren/Hrsg.

Hanßmann, Heinz

Fachgebiete

• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

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.