Heinz Hanβmann (auth.)9783540388944, 3-540-38894-X, 354038894X
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. |
Table of contents :
Front Matter….Pages I-XV
Introduction….Pages 1-15
Bifurcations of Equilibria….Pages 17-89
Bifurcations of Periodic Orbits….Pages 91-107
Bifurcations of Invariant Tori….Pages 109-142
Perturbations of Ramified Torus Bundles….Pages 143-159
Planar Singularities….Pages 161-165
Stratifications….Pages 167-171
Normal Form Theory….Pages 173-184
Proof of the Main KAM Theorem….Pages 185-200
Proofs of the Necessary Lemmata….Pages 201-206
Back Matter….Pages 207-241 |
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