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A note on Gevrey regular KAM theory and the inverse approximation lemma. (English) Zbl 1036.37022

Summary: A theorem of the type Kolmogorov-Arnold-Moser holds for small real analytic perturbations of a family of parallel flows on a torus, yielding conjugacies to Diophantine parallel flows that depend Whitney-Gevrey regularly on parameters. This follows from an adaptation of the inverse approximation lemma. The method of proof is general and extends to a wide range of problems of KAM type.

MSC:

37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion
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References:

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