01286nas a2200157   4500008004100000020001400041245006600055210006500121260001500186300001600201490000800217520081700225100001801042700002101060856004701081       2019                        eng d  a1618-189100aReducibility for a fast-driven linear Klein–Gordon equation0 aReducibility for a fastdriven linear Klein–Gordon equation  c2019/08/01  a1407 - 14390 v1983 a<p>We prove a reducibility result for a linear Klein–Gordon equation with a quasi-periodic driving on a compact interval with Dirichlet boundary conditions. No assumptions are made on the size of the driving; however, we require it to be fast oscillating. In particular, provided that the external frequency is sufficiently large and chosen from a Cantor set of large measure, the original equation is conjugated to a time-independent, diagonal one. We achieve this result in two steps. First, we perform a preliminary transformation, adapted to fast oscillating systems, which moves the original equation in a perturbative setting. Then, we show that this new equation can be put to constant coefficients by applying a KAM reducibility scheme, whose convergence requires a new type of Melnikov conditions.</p>1 aFranzoi, Luca1 aMaspero, Alberto  uhttps://doi.org/10.1007/s10231-019-00823-2