Gevrey asymptotics of series in Mourtada-type compensators used for linearization of an analytic 1:−1 resonant saddle

Given a 1:−1 resonant saddle singularity of a planar analytic vector field, we provide a linearization procedure using a series expansion in compensators of Mourtada-type, and show that this series has Gevrey-1 asymptotics. In case of an analytic Poincaré-Dulac normal form we show that this transformation is analytic as a function of the compensators.