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Critical Behavior of a KAM surface. I: Empirical results. (English) Zbl 0925.58021
Summary: Kolmogorov - Arnold - Moser (KAM) surfaces are studied in the context of a perturbed two-dimensional twist map. In particular, we ask how a KAM surface can disappear as the perturbation parameter is increased. Following Greene, we use cycles to numerically construct the KAM curve and discover that at the critical coupling it shows structure at all length scales. Aspects of this structure are fitted by a scaling analysis; critical indices and scaling functions are determined numerically. Some evidence is presented which suggests that the results are universal.

MSC:
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
70K50 Bifurcations and instability for nonlinear problems in mechanics
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