1991 | OriginalPaper | Chapter
Birth and Death of Invariant Tori for Hamiltonian Systems
Author : Luigi Chierchia
Published in: The Geometry of Hamiltonian Systems
Publisher: Springer US
Included in: Professional Book Archive
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The stability of invariant tori with (highly) irrational periods in the context of nearly integrable Hamiltonian systems and symplectic diffeomorphysms is considered. A theorem, based on computer-assisted implementations of recent KAM techniques, establishing the persistence of “golden-mean-tori” for “large” values of the nonlinearity parameter ε in two paradigmatic models is presented. Numerical investigations on the distribution of complex singularities in the parameter e indicates that the method of proof, which involves the explicit construction of approximating surfaces, is optimal at least in the models considered here.