One of the most powerful and versatile tools in the study of invariant surfaces for conservative dynamical systems relies upon KAM theory (, , , , , , , ). However, because of the apparently stringent quantitative requirements, such theory has been (and often still is) considered not too well suited for concrete applications. Nevertheless, in , , ,  and especially in , , , , it has been shown how refinements and implementations of KAM theory may yield quantitative rigorous results that are in good agreement with the numerical expectations.
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