  We study hyperbolized versions of cohomological equations that appear with
cocycles by isometries of the euclidean space. These (hyperbolized versions of)
equations have a unique continuous solution. We concentrate in to know whether
or not these solutions converge to a genuine solution to the original equation,
and in what sense we can use them as good approximative solutions. The main
advantage of considering solutions to hyperbolized cohomological equations is
that they can be easily described, since they are global attractors of a
naturally defined skew-product dynamics. We also include some technical results
about twisted Birkhoff sums and exponential averaging.
