Local and semi-local bifurcations in Hamiltonian dynamical systems : results and examples
著者
書誌事項
Local and semi-local bifurcations in Hamiltonian dynamical systems : results and examples
（Lecture notes in mathematics, 1893）
Springer, c2007
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注記
Includes bibliographical references (p. [219]-233) and index
内容説明・目次
内容説明
This book demonstrates that while elliptic and hyperbolic tori determine the distribution of maximal invariant tori, they themselves form n-parameter families. Therefore, torus bifurcations of high co-dimension may be found in a single given Hamiltonian system, absent untypical conditions or external parameters. The text moves logically from the integrable case, in which symmetries allow for reduction to bifurcating equilibria, to non-integrability, where smooth parametrisations must be replaced by Cantor sets.
目次
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.
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