  We consider a Froeschl\'e map and we add a weak dissipation of the form
$\lambda(\varepsilon) = 1- \varepsilon^3$, where $\varepsilon$ is the parameter
of perturbation. We compute formal expansions of lower dimensional tori, both
in the conservative and weakly dissipatives cases, and use them to estimate the
shape of their domains of analyticity as functions of $\varepsilon$. Our
results support conjectures in the literature.
