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- W4299477922 abstract "A fundamental question in Dynamical Systems is to identify regions of phase/parameter space satisfying a given property (stability, linearization, etc). Given a family of analytic circle diffeomorphisms depending on a parameter, we obtain effective (almost optimal) lower bounds of the Lebesgue measure of the set of parameters that are conjugated to a rigid rotation. We estimate this measure using an a-posteriori KAM scheme that relies on quantitative conditions that are checkable using computer-assistance. We carefully describe how the hypotheses in our theorems are reduced to a finite number of computations, and apply our methodology to the case of the Arnold family. Hence we show that obtaining non-asymptotic lower bounds for the applicability of KAM theorems is a feasible task provided one has an a-posteriori theorem to characterize the problem. Finally, as a direct corollary, we produce explicit asymptotic estimates in the so called local reduction setting (`a la Arnold) which are valid for a global set of rotations." @default.
- W4299477922 created "2022-10-02" @default.
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- W4299477922 date "2018-06-14" @default.
- W4299477922 modified "2023-09-27" @default.
- W4299477922 title "Effective bounds for the measure of rotations" @default.
- W4299477922 doi "https://doi.org/10.48550/arxiv.1806.05517" @default.
- W4299477922 hasPublicationYear "2018" @default.
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