Haro, ÀlexLuque, Alejandro, 1974-Figueras, Jordi-Lluís2023-01-272023-01-272019-12-190951-7715https://hdl.handle.net/2445/192675A 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 (à la Arnold) which are valid for a global set of rotations.42 p.application/pdfeng(c) IOP Publishing & London Mathematical Society , 2019Sistemes dinàmics de baixa dimensióTeoria ergòdicaAnàlisi numèricaAnàlisi d'intervals (Matemàtica)Low-dimensional dynamical systemsErgodic theoryNumerical analysisInterval analysis (Mathematics)info:eu-repo/semantics/article6999712023-01-27info:eu-repo/semantics/openAccess