Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems

• Main Author: Hanβmann, Heinz (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2007.
• Series: Lecture Notes in Mathematics, 1893
• Subjects: Mathematics.; Dynamics.; Ergodic theory.; Global analysis (Mathematics).; Manifolds (Mathematics).; Differential equations.; Physics.; Dynamical Systems and Ergodic Theory.; Ordinary Differential Equations.; Global Analysis and Analysis on Manifolds.; Theoretical, Mathematical and Computational Physics.

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, tor...

Table of Contents:

• 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.