Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems : Results and Examples
- Author
- Heinz Hanβmann
- Publication Year
- 2007
- Publisher
- Springer
- Language
- English
- Document Type
- Book
- Faculty / Subject Heading
- Mathematics and Statistics
- Download Book Read book
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.
Keywords: Mathematics and Statistics / Cantor / Invariant /KAM Theory / Dynamical systems / Multiparameter bifurcation / Proof / Ramified torus bundle / Symmetry reduction / Theorem / Versal unfolding
