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.
• Physical Description: XVI, 242 p. 22 illus. online resource.
• ISBN: 9783540388968
• ISSN: 0075-8434 ;

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.