Local and semi-local bifurcations in Hamiltonian dynamical systems : results and examples
Heinz Hanssmann
Bok Engelsk 2007
| Annen tittel | |
|---|---|
| Utgitt | Berlin : Springer , c2007
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| Omfang | 1 online resource (XVI, 242 p. 22 illus.)
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| Opplysninger | Bibliographic Level Mode of Issuance: Monograph. - 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.. - 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.
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| Emner | |
| Dewey | |
| ISBN | 354038894X. - 9783540388944
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