20-11 Renato C. Calleja, Alessandra Celletti, Rafael de la Llave

KAM estimates for the dissipative standard map (675K, PDF) Mar 4, 20

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Abstract. From the beginning of KAM theory, it was realized that its applicability to realistic problems depended on developing quantitative estimates on the sizes of the perturbations allowed. In this paper we present results on the existence of quasi-periodic solutions for conformally symplectic systems in non-perturbative regimes. We recall that, for conformally symplectic systems, finding the solution requires also to find a mph{drift parameter}. We present a proof on the existence of solutions for values of the parameters which agree with more than three figures with the numerically conjectured optimal values. The first step of the strategy is to establish a very explicit quantitative theorem in an a-posteriori format. We recall that in numerical analysis, an a-posteriori theorem assumes the existence of an approximate solution, which satisfies an invariance equation up to an error which is small enough with respect to explicit condition numbers, and then concludes the existence of a solution. In the case of conformally symplectic systems, an a-posteriori theorem was proved in

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